Pricing in general insurance

PRICING IN GENERAL INSURANCE PRICING IN GENERAL INSURANCE Pietro Parodi CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20140626 International Standard Book Number-13: 978-1-4665-8148-7 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To my parents, for their unfailing support and patience over the years; to my sister, for her constant encouragement; and to Vincent, for his lasting and undiminishing intellectual influence Contents Preface xxiii Acknowledgements xxv Section I  Introductory Concepts Pricing Process: A Gentle Start 1.1 An Elementary Pricing Example 1.1.1 Risk Costing (Gross) 1.1.1.1 Adjusting for ‘Incurred but Not Reported’ Claims 1.1.1.2 Adjusting for Claims Inflation 1.1.1.3 Adjusting for Exposure Changes 1.1.1.4 Adjusting for Other Risk-Profile Changes 1.1.1.5 Adjusting for ‘Incurred but Not Enough Reserved’ Claims 1.1.1.6 Changes for Cover/Legislation 10 1.1.1.7 Other Corrections 10 1.1.2 Risk Costing (Ceded) 11 1.1.3 Determining the Technical Premium 11 1.1.3.1 Loading for Costs 11 1.1.3.2 Discounting for Investment Income 11 1.1.3.3 Loading for Capital/Profit 12 1.1.4 Commercial Considerations and the Actual Premium 12 1.1.5 Limitations of This Elementary Pricing Example 13 1.2 High-Level Pricing Process 13 1.3 Questions 14 Insurance and Reinsurance Products 17 2.1 Classification of General Insurance Products: General Ideas 17 2.2 Products by Category of Cover 18 2.2.1 Property Insurance 18 2.2.1.1 Legal Framework 18 2.2.1.2 Pricing Characteristics 19 2.2.1.3 Examples of Property Policies 20 2.2.2 Liability Insurance 20 2.2.2.1 Legal Framework 20 2.2.2.2 Pricing Characteristics 22 2.2.2.3 Examples of Liability Insurance 22 2.2.3 Financial Loss Insurance 23 2.2.3.1 Examples 23 2.2.3.2 Pricing Characteristics 23 2.2.4 Fixed Benefits Insurance 23 2.2.4.1 Examples 23 2.2.4.2 Pricing Characteristics 23 2.2.5 ‘Packaged’ Products 24 vii viii Contents 2.3 Products by Type of Customer 24 2.3.1 Personal Lines 24 2.3.1.1 Examples 24 2.3.1.2 Pricing Characteristics 24 2.3.2 Commercial Lines 25 2.3.2.1 Examples 25 2.3.2.2 Pricing Characteristics 26 2.3.3 Reinsurance 26 2.3.3.1 Examples 26 2.3.3.2 Pricing Characteristics 27 2.4 Prudential Regulation Authority Classification 27 2.5 Other Classification Schemes 38 2.6 Non-Extant Products 38 2.7 Questions 38 The Policy Structure 41 3.1 Personal Lines 41 3.1.1 Purpose of the Excess Amount 42 3.1.2 Purpose of the Limit .43 3.2 Commercial Lines 43 3.2.1 Policy Bases 43 3.2.1.1 Occurrence Basis 43 3.2.1.2 Claims-Made Basis 43 3.2.1.3 Other Bases 44 3.2.2 Basic Policy Structure 44 3.2.2.1 Each-and-Every-Loss Deductible 44 3.2.2.2 Annual Aggregate Deductible 44 3.2.2.3 Each-and-Every-Loss Limit 45 3.2.3 Other Coverage Modifiers 49 3.2.3.1 Non-Ranking Each-and-Every-Loss Deductible 49 3.2.3.2 Residual Each-and-Every-Loss Deductible 49 3.2.3.3 Quota Share 49 3.2.3.4 Yet-More-Exotic Coverage Modifiers 50 3.3 Reinsurance 50 3.3.1 Policy Bases 50 3.3.1.1 Losses Occurring During 50 3.3.1.2 Risk Attaching During 50 3.3.1.3 Claims Made 51 3.3.2 Non-Proportional Reinsurance 51 3.3.2.1 Risk Excess of Loss 51 3.3.2.2 Aggregate Excess of Loss 55 3.3.2.3 Catastrophe Excess of Loss 55 3.3.2.4 Stop Loss Reinsurance 57 3.3.3 Proportional Reinsurance 58 3.3.3.1 Quota Share 58 3.3.3.2 Surplus Reinsurance 58 3.4 Questions 59 522 Pricing in General Insurance Volatility (VaR@99.5%) [£] Efficient vs Inefficient Insurance Structures 280,000,000 B 260,000,000 240,000,000 C 220,000,000 200,000,000 180,000,000 A 160,000,000 140,000,000 120,000,000 100,000,000 30,000,000 40,000,000 50,000,000 60,000,000 70,000,000 80,000,000 Premium [£] FIGURE 29.1 Each insurance structure can be represented as a light-grey dot in this cost–benefit chart, in which the cost is the insurance premium and the benefit is in this case measured by the value at risk at the 99.5th percentile The dark grey dots lie on the so-called efficient frontier B and C are not efficient and they can both be improved by purchasing A instead 29.1.4 Limitations of the Efficient Frontier Approach • The big problem with the efficient frontier approach is that you need to know the premium for a large number of structures In practice, this is normally replaced with an estimated premium calculated with a formula (For example, a loss ratio may be estimated based on a few actual quotes, and then the premium for the other structures may in turn be estimated by dividing the expected ceded losses by that loss ratio.) Therefore, once an actual quote is obtained for the chosen structure, it might turn out to be less (or more) convenient than initially thought • Using a different metric (or even the same metric with different parameters, such as VaR@95% and VaR@99%) will lead to a different efficient frontier • One issue that risks being concealed under the calculations and not communicated properly to clients is that of the uncertainty in the estimate of the expected retained and (especially) of the volatility Because of data, parameter, and model uncertainty, the efficient frontier is actually a much fuzzier object than a line! • The method does not offer us a ‘best option’ – just a range of noncomparable efficient options 29.2 Minimising the Total Cost of (Insurable) Risk One of the limitations that we have mentioned in Section 29.1.4 about the efficient frontier method is that it does not actually select a specific structure, it just yields a set of noncomparable efficient structure This is a consequence of the fact that volatility and premium are two different criteria to judge insurance structures, and no way is provided to weigh one against the other To have a criterion that allows us to compare any two insurance structures, we need to be able to assign a single real number to each insurance structure One commonly used method to achieve this is through the so-called ‘total cost of risk’ First of all, note that we are interested here in the total cost of insurable risk: not because Insurance Structure Optimisation 523 uninsurable risk is less significant, but because we are currently looking at how the selection of an appropriate level of retention for your insurance structure can be made optimal Uninsurable risks are also important and are part of the problems that the risk management department of a company must face 29.2.1 Risk Management Options Before we define the total cost of risk, let us discuss what an individual or a company needs to to address risks After identifying and measuring one particular risk, one has several options for dealing with risks: • Ignore it – it may sound silly to include this as an option, but this is a perfectly legitimate option in the face of risk, and arguably most risks are ignored by people and organisations if they are perceived as too remote For example, a company may buy employers’ liability cover up to £50M but ignore anything beyond that – judging the likelihood of a claim higher than that limit occurring too small to be concerned about We this all the time in our lives – we may be pursuaded to follow a lower-fat diet to reduce the probability of heart disease, but we may decide to take no action to reduce the risk of rare diseases that affect one person in 100,000 One just accepts that awful things can happen without doing anything about it if the likelihood is small enough • Retain it – this might look very much like ‘ignore it’, because ultimately you are going to be the one who pays the consequences of either ignoring or retaining the risk There is a difference, though: when you retain a risk, you manage it consciously, for example, by making sure you have money aside to pay for a large claim should such a claim happen • Transfer it – this normally means that you buy insurance to protect yourself against the risk However, other ways of transferring are possible, for example, to the capital markets or to a parent company • Mitigate/prevent it – this means that you are setting up risk control mechanisms, such as (in the case of property risk) fire detection systems, firewalls, disaster recovery sites and the like, either to prevent the risk or to mitigate its effects after the event has occurred • Adopt a mixture of the strategy above – as we will see, the most common way of dealing with risk is by adopting a hybrid solution, that is, by actually doing some or all of the things above Different risk strategies will simply shift the emphasis from one of the risk management options to another 29.2.2 Total Cost of Risk: Definition All of these options (except for ‘ignore’) have a cost, and all (including ‘ignore’) have consequences In general, we can write down the total cost of risk (TCR) for a hybrid risk management strategy as the sum of all the costs for the options above: Total cost of risk = Cost of retaining + Cost of transferring + Cost of mitigating/preventing (29.1) 524 Pricing in General Insurance Because we wish to focus on the differences between different insurance structures, we can assume that the cost of mitigating/preventing bit is roughly constant across different insurance structures (either because the company wills it or because the insurer requires a certain level of health and safety to issue insurance), and therefore ignore the term Also, the cost of retaining a risk can be split into two terms, one for normal, day-to-day smaller losses (the so-called ‘expected’ losses) and the other for holding capital for a bad year We can therefore rewrite the total cost of risk as Total cost of risk = cost of retaining smaller losses + cost of holding capital for a bad year + cost of transferring (29.2) This is the general structure of the total cost of risk, which we can all relate to After all, this is what we all when dealing with risk as customers: insure part of it, keep the smaller losses that not affect our ability to get to the end of the month, and possibly put some money aside just if an unexpected outgoing is called for For the sake of choosing between insurance structures, however, we need to be a bit more precise What are smaller, normal losses? What is a bad year? What is the cost of holding capital? There is no unique answer to these questions, and therefore no unique formula for the total cost of risk However, a commonly adopted definition is this: Total cost of risk = mean retained losses + CoC × (VaR@p% − mean retained losses) + insurance premium (29.3) where: VaR@p% is the pth percentile of the retained loss distribution CoC is the cost of capital, that is, the opportunity cost of freezing an amount equal to VaR@p% minus mean expected losses of capital to pay possible claims (rather than investing it into the business) p is called the safety level, or risk tolerance level, or ‘ignore’ threshold, and represents the level of probability beyond which the company is happy to ignore the consequences of retaining risk.* For example, if p = 99%, that means that the company is happy to be safe in 99% of the cases, and to ignore events that happen with less than 1% probability Note that the ‘frozen capital’ is just the capital that you have to put aside in excess of the normal, expected losses One problem with this definition is that, especially in the case of excess layers with a large attachment point, some insurance structures may have a value at risk that is actually lower than the mean retained It would therefore make more sense to replace the mean retained losses with the median retained losses (which can also be written as VaR@50%), which are guaranteed to be less than or equal to the value at risk at any percentile higher than 50% Also, VaR@p% can be replaced with other measures of volatility, such as the tail value at risk In this case, the tail value at risk for any p is always greater than the mean retained (which is, incidentally, equal to TVaR@0%), and therefore it is not necessary to replace the mean retained with the median retained Note that, in the case of the TVaR, the risk with probability less than 1−p is not really ignored! * This is true, at least, if the value at risk (which ignores whatever happens beyond a given percentile) is used as a risk measure For other risk measures, the interpretation of the safety level is more complex Insurance Structure Optimisation 525 The list below contains some other legitimate definitions for the total cost of risk, each of which has its own advantages and disadvantages (Question 3) a TCR = median retained + premium + CoC × (VaR@p% − median losses) = VaR@50% + premium + CoC × (VaR@p% − VaR@50%) b TCR = mean retained + premium + CoC × (VaR@p% − median losses) c TCR = mean retained + premium + CoC × (TVaR@p% − mean retained) = TVaR@0% + premium + CoC × (TVaR@p% − TVaR@0%) (29.4) 29.2.3 Choosing the Optimal Structure Whatever the definition of TCR we use, TCR will enable us to associate a number to an insurance structure, no matter how complicated that is As a result, this will make any two insurance structures comparable, and will give us a simple recipe for selecting the best insurance option Consider that, in doing this analysis, you are adopting the perspective of someone who is going to purchase insurance (or otherwise manage their risks) and you are advising them as to what their best option is If you this type of analysis, it will be because you are a consultant or a broker hired by a company, or because you are a member of the risk/ insurance management team of that company (in any case, the client is the company itself) In the case of reinsurance, replace ‘company’ with ‘insurer’, and ‘risk/insurance management team’ with ‘risk/reinsurance management team’ 29.2.3.1 Selecting the Best Insurance Option amongst K Options a Choose a safety level p, based on the client’s risk tolerance level (this should normally be part of a discussion with the client) This level should be set as discussed in Section 29.2.1, by considering how unlikely the risk has to be for the client to be happy to ignore them b Choose a CoC, again after discussion with the client, who is in the best position to advise what their CoC is c Consider all the K alternative insurance structures and, for each of them, estimate the premium (if not available) and calculate the total cost of risk by Equation 29.3 d Impose any additional constraints as required by the client, such as maximum premium, minimum/maximum retention levels, or as dictated by the market, such as availability of certain limits of cover, and minimum premium e The optimal insurance structure is that with the lowest value of the total costs of risk among those which satisfy the constraints Note that it is still possible to have more than one insurance structure with exactly the same total cost of risk In this case, any of these structures would be equally viable 29.2.4 Total Cost of Risk Calculation: A Simple Example Assuming we use the standard definition of the total cost of risk given in Equation 29.3, let us see how the total cost of risk can be calculated in a very simple situation First of all, consider a single insurance structure, a very simple one with no deductible, no policy limit, 526 Pricing in General Insurance 10% 20% 30% 40% 50% 60% 70% 80% 90% 95% 97.50% 98% 99% 99.50% 99.90% Mean Gross 2853 13,022 34,533 87,656 198,404 438,636 932,732 2,354,382 7,853,838 20,327,166 65,800,598 79,013,718 256,961,796 923,918,924 4,295,518,341 14,977,284 Retained 2853 13,022 34,533 87,656 198,404 438,636 932,732 2,354,382 7,853,838 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 1,720,527 Ceded – – – – – – – – – 10,327,166 55,800,598 69,013,718 246,961,796 913,918,924 4,285,518,341 13,256,757 Estimated premium (with LR=50%) 26,513,513 FIGURE 29.2 The aggregate distribution of gross, retained, and ceded losses for a very heavy-tailed risk and an AAD of £10M Assume that the distribution of gross, ceded, and retained losses is as in Figure 29.2 (the distribution has been deliberately chosen so that it has a very heavy tail, to make the effect of the AAD clear) From a conversation with the client, it has emerged that their risk tolerance level is 97.5% (i.e they wish to ignore anything that happens with a probability smaller than 2.5%), and that their CoC is 10% You not have a quoted premium but you estimate that the underwriter will be seeking a loss ratio of 50%, which leads you to estimate a premium of £26.5M (premium = mean ceded losses/loss ratio) Question: Before reading on, what is your estimate of the total cost of risk? By using Equation 29.3, the total cost of risk can be calculated as TCR = premium + mean retained + CoC × (VaR@97.5% − Mean Retained) = £26.5M + £1.7M + 0.1 × (£10.0M − £1.7M) = £29.0M Next, we wonder if this structure is optimal We want to limit ourselves (for the sake of keeping the calculations simple) to structures that have no each-and-every-loss deductible and no policy limit, but different values of the AAD We then try out a large number of aggregate deductibles between £1M and £33M and, for each of them, we calculate the total cost of risk by recalculating the mean retained losses, the premium (by dividing the mean ceded by the loss ratio of 50%), and the value at risk at 97.5% The results are shown in Figure 29.3 It turns out that the ‘optimal’ structure has AAD ~ £8M (which corresponds to an annual cap that is going to be hit with a probability of roughly 10%) However, it should be noted that any value in the region of £5M to £10M will yield similar results in terms of TCR 527 33,000,000 31,000,000 29,000,000 27,000,000 25,000,000 23,000,000 21,000,000 19,000,000 17,000,000 15,000,000 13,000,000 9,000,000 11,000,000 7,000,000 5,000,000 3,000,000 Total Cost of Risk vs Agg Deductible 30,800,000 30,600,000 30,400,000 30,200,000 30,000,000 29,800,000 29,600,000 29,400,000 29,200,000 29,000,000 28,800,000 1,000,000 Total cost of risk [£] Insurance Structure Optimisation Annual aggregate deductible [£] FIGURE 29.3 The estimated TCR for a large number of different structures, all of them identical except for the value of the AAD Notice the minimum at approximately £8M Therefore, even though our current structure (AAD = £10M) is not optimal, it is nearoptimal, and only a comparison of the actual (rather than estimated) premiums of the two structures will help us decide between the two 29.2.5 Relationship between Total Cost of Risk and Efficient Frontier How is the total cost of risk related to the efficient frontier? If you use the same measure of volatility and the same reference percentage (e.g VaR@99%), then it seems sensible to expect that the structure with the optimal TCR will lie on the efficient frontier Is that actually the case? First of all, let us rewrite the TCR as follows: TCR = P + E(Sret ) + CoC( VaR@p − E(Sret )) = P + (1 − CoC) × E(Sret ) + CoC × VaR@p = P − (1 − CoC) × E(Sced ) + (1 − CoC) × E(S) + CoC × VaR@p Assume that a structure Σ has the lowest cost of risk but does not lie on the efficient frontier Then there will be another structure Σ′ with the same value of VaR@p, which does lie on the efficient frontier and therefore has premium P′ < P, and of course E(Sced ′ ) < E(Sced ) (unless it is possible to pay less by ceding more!) Now if we can assume that P − P′ > (1 − CoC) × E ( Sced ) − E ( Sced ′ ) , that is, that it is not possible to obtain £1 of reduction in the ceded losses by paying less than £1*, then TCR′ < TCR, which contradicts the assumption that Σ was optimal Therefore, under rather broad assumptions on the loss ratio, we see that the optimal structure from the TCR point of view also lies on the efficient frontier ( ) 29.2.6 Limitations The total cost of risk has several limitations, some of which are exactly the same as the limitations of the efficient frontier approach * This is immediately true if we can assume that the same loss ratio will apply to both structures, and that such loss ratio is lower than 1/(1 − CoC), which is a number larger than 528 Pricing in General Insurance • As in the case of the efficient frontier methodology, it is only possible to obtain actual premiums or desk quotes for a few structures; most of the premiums will be obtained by a simple formula based on a few desk quotes/actual quotes, for example, assuming a loss ratio • The mean retained and the ‘Retained@safety level’ is also only an estimate based on a loss model, with its usual uncertainties (model, parameter, data…) – the total cost of risk is actually fuzzy • Using a different metric for the ‘Retained@safety level’ bit (or even the same metric with different parameters, for example, VaR@95% and VaR@99%) will yield a different TCR and a different optimal structure • Structures that are quite different will tend to yield very similar values of the TCR, which (added to the uncertainty around the TCR) makes one wonder about the discriminatory power of TCR minimisation as an optimality criterion 29.3 Questions Consider the following list of insurance structures and highlight those that are surely inefficient using VaR@99% as a measure of volatility: a Structure 1: premium = £1.2M, VaR@99% = £99M b Structure 2: premium = £1.7M, VaR@99% = £78M c Structure 3: premium = £1.3M, VaR@99% = £105M d Structure 4: premium = £4M, VaR@99% = £50M e Structure 5: premium = £4.5M, VaR@99% = £50M Company X has traditionally purchased public liability insurance from the ground up, but to decrease the insurance premium (currently at £2,500,000) spend and in view of its financial robustness, it is now investigating the opportunity of retaining the portion of each loss, which is below a given amount (‘each and every loss [EEL] deductible’) The company has obtained these two quotes for insurance at these different levels of deductibles: • EEL = £100K → Premium = £900,000 • EEL = £200K → Premium = £450,000 The company asks a consultant what level of EEL they should choose, and the consultant proposes to choose the level of EEL that minimises the ‘total cost of risk’ i State the formula for the total cost of risk The company gives the consultant this further information: −− They are not worried about overall level of retained losses that happen with a probability of less than 1% (on an annual basis) −− The company’s CoC is 12% ii Explain what the CoC is An actuarial analysis gives the following estimates of the gross, retained and ceded distributions for different levels of EEL 2,380,186 2,510,521 2,903,459 3,274,703 3,779,592 4,152,528 4,495,618 4,791,922 4,991,777 1,969,444 718,000 80% 90% 95% 98.0% 99.0% 99.5% 99.8% 99.9% Mean Std Dev 1,869,704 75% 50% Total loss Percentile 0 0 0 0 0 0 Retained 718,000 1,969,444 4,991,777 4,791,922 4,495,618 4,152,528 3,779,592 3,274,703 2,903,459 2,510,521 2,380,186 1,869,704 Ceded EEL = £0 308,145 1,223,767 2,319,460 2,231,156 2,103,179 1,999,685 1,892,509 1,754,710 1,633,268 1,478,409 1,424,166 1,205,151 Retained 525,032 745,676 3,468,427 3,303,707 2,842,877 2,466,066 2,164,576 1,743,826 1,434,902 1,095,454 983,601 634,128 Ceded EEL = £100k 448,452 1,602,097 3,204,756 3,080,203 2,897,132 2,766,417 2,608,209 2,383,344 2,196,113 1,973,002 1,887,698 1,573,081 Retained 412,922 367,346 2,918,832 2,689,858 2,210,172 1,887,943 1,547,230 1,166,614 885,675 600,654 516,466 244,834 Ceded EEL = £200k 610,099 1,882,367 4,121,569 3,982,094 3,740,428 3,576,709 3,316,971 2,968,721 2,682,736 2,385,498 2,268,864 1,823,682 Retained 243,299 87,077 2,236,319 1,977,433 1,476,792 1,188,535 880,550 527,750 278,422 92,638 37,675 Ceded EEL = £500k Insurance Structure Optimisation 529 530 Pricing in General Insurance The company also asks the consultant to estimate what the premium will be if the EEL should be £500K The consultant produces the following desk quote: −− EEL = £500K → Premium = £120,000 iii Explain what a desk quote is iv Based on the information provided, determine the best of the four options (no EEL, EEL = £100K, EEL = £200K, or EEL = £500K) from a total cost of risk’s perspective, explaining your reasoning v Explain what the main uncertainties around this result are Explain the rationale behind the four different possible formulations of the total cost of risk given in Equations 29.3 and 29.4, and their relative 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GENERAL INSURANCE Based on the syllabus of the actuarial industry course on general insurance pricing — with additional material inspired by the author’s own experience as a practitioner and lecturer — Pricing in General Insurance presents pricing as a formalised process that starts with collecting information about a particular policyholder or risk and ends with a commercially informed rate The main strength of this approach is that it imposes a reasonably linear narrative on the material and allows the reader to see pricing as a story and go back to the big picture at any time, putting things into context Written with both the student and the practicing actuary in mind, this pragmatic textbook and professional reference: • • • • Complements the standard pricing methods with a description of techniques devised for pricing specific products (e.g., non-proportional reinsurance and property insurance) Discusses methods applied in personal lines when there is a large amount of data and policyholders can be charged depending on many rating factors Addresses related topics such as how to measure uncertainty, incorporate external information, model dependency, and optimize the insurance structure Provides case studies, worked-out examples, exercises inspired by past exam questions, and step-by-step methods for dealing concretely with specific situations Pricing in General Insurance delivers a practical introduction to all aspects of general insurance pricing, covering data preparation, frequency analysis, severity analysis, Monte Carlo simulation for the calculation of aggregate losses, burning cost analysis, and more K18873 w w w c rc p r e s s c o m [...]... pricing actuary in general insurance And apart from the historical impossibility (actuaries were first involved in general insurance around 1909 in the United States, to deal with workers’ compensation insurance) , the job of the pricing actuary in general insurance is way too exciting – contrary perhaps to public perception – to be described as mindless drudgery: pricing risk means understanding risk and... operates in This book is based on my experience as both a practitioner and a part-time lecturer at Cass Business School in London It was written to communicate some of the excitement of working in this profession and to serve the fast-expanding community of actuaries involved in general insurance and especially in pricing It comes at a time when this relatively new discipline is coming of age and pricing. .. ST8 exam ( General Insurance Pricing ) of the Actuarial Profession in the United Kingdom and India, with additional material xxiii xxiv Preface Pricing as a Process One of the main efforts of this book is to present pricing as a process because pricing activity (to an insurer) is never a disconnected bunch of techniques, but a more-or-less formalised process that starts with collecting information... is switching from another area of practice (such as pensions) to hit the ground running when starting to work in general insurance At the same time, the fact that there is roughly a chapter for each building block of the detailed risk pricing process should help the practitioner who is already involved in general insurance pricing to use this textbook as a reference and explore each technique in depth... types of insurance or reinsurance product, such as exposure rating for property reinsurance If the student has started becoming a bit dogmatic about the pricing process at the end of Section II, and has started thinking that there is only one correct way of doing things, this part offers redemption: the student learns that tweaking the process is good and actually necessary in most practical cases Finally,... executed in a certain order To get a fair idea of what the pricing process entails without getting bogged down into the details that inevitably need to be considered in any realistic example, we will start looking at a very simple example of pricing, carried out in a rather traditional, non-actuarial way Despite its simplicity, this example will contain all the main ingredients of the pricing process... 5.7.2 Underwriting Function 86 5.7.3 Claims Function 86 5.7.3.1 Interaction with the Pricing Function 86 5.7.4 Actuarial: Reserving 86 5.7.4.1 Interaction with the Pricing Function 87 5.7.5 Actuarial: Capital Modelling 87 5.7.5.1 Interaction with the Pricing Function 87 5.7.6 Finance 87 5.7.6.1 Interaction with the Pricing Function... emphasis always being on how things can be done in practice, and what the issues in the real world are Alternative, more traditional ways of pricing (such as burning cost analysis) are also explored After learning the language of pricing, one can start learning the dialects; Section III: Elements of Specialist Pricing goes beyond the standard process described in Section II and is devoted to pricing methods... (all the reinsurance content and frequency/severity modelling), Raheal Gabrasadig (introductory chapters), Chris  Gingell (energy products), Torolf Hamm (catastrophe modelling), Anish Jadav (introductory example, products), Joseph Lees (burning cost), Marc Lehmann (catastrophe modelling), Joseph  Lo (from costing to pricing, plus all the introductory chapters),  Eamonn  McMurrough (pricing control... Exposure Rating Process in Reinsurance 341 21.7.1 Basic Process 342 21.7.2 How This Is Done in Practice 343 21.7.2.1 Sources of Uncertainty .345 Contents xvii 21.7.3 Making It Stochastic 347 21.7.3.1 Calculation of the Aggregate Loss Distribution Using Exposure Rating 347 21.8 Using Exposure Rating in Direct Insurance 349 21.8.1 Hybrid Rating: