## 1. 3. Deterministic and stochastic models

### 1.1. features of the deterministic modelling process

1.1.1. Key features: *parameters have fixed values *results are in the form of a point estimate *Sensitivity testing possible by running with different parameters

### 1.2. features of the stochastic modelling process

1.2.1. *Some parameters are allowed to vary (no claims or claim amounts) allowed to vary and have own distribution functions *run many times using random samples from distn functions *results in form of a probability distn Health care less easy to predict future incidence of experience, potential benefit amount can vary by policy specified inflation (LTCI, IP), medical inflation (PMI) changes in accepted medical protocols or other factors. Uncertainty/volatility of cashflows need to be able to predict distribution of outcomes.

### 1.3. choosing between stochastic and deterministic approaches

1.3.1. Stoch: +impact of guar assessment +Variable of interest has stable predictable distn function +indicating the year on year volatility (random fluctuations) +identifying potential high risk future scenarios (tracing the sequence of worst scenarios) -time and computing constraints -sensitivity of results to the deterministically chosen parameters i.e. normal distn with mean and variance deterministically calculated. Spurious accuracy, complexity, false sense of security.

### 1.4. Calibration of stochastic models

1.4.1. Approaches to setting parameters: 1. Risk Neutral (market consistent) calibration - typically used for valuation purposes, particularly where there is options and guarantees. focus is on replicating market prices of actual financial instrumentals as closely as possible using adjusted (risk neutral) probability measure. steps: chose number of financial instruments (derivatives usually). Project CF using model in range of scenarios. PV of CF from simulation are close to market price (by chosing parameters). Idea- market can replicate asset prices, it should be able to provide values for unquoted assets or liabilities 2. Real world calibration - used for projecting into future, e.g. calculating level of capital to hold to ensure solvency under extreme adverse scenarios at given confidence level. use assumptions that reflect realistic 'long term' expectations and that consequently reflect real world probabilities and outcomes. using expectations of the future. Assumptions then used to project assets and liabilities.

## 2. 4. Sensitivities

### 2.1. sensitivity to choice of model point

2.1.1. *less then ideal model points used, have to assess choice by sensitivity testing *If large enough no of models, less model point error risk. larger, longer time to do model runs.

### 2.2. Sensitivity to parameters

2.2.1. *effect of mis-estimation of parameters can be investigated by sensitivity analysis *Correlations should be allowed for i.e. adjusting parameters together that are linked - scenario testing. *mis-estimation - actual future experience being different then expected. *get financial impact of parameters of most uncertainty- design product so it becomes insensitive to this feature, else, margins.

### 2.3. Sensitivity when pricing

2.3.1. *assess what margins need to be incorporated into parameter values *Profit sensitivity to any factor may indicate redesign require or other measures. e.g. sensitive to withdrawal rates, change commission structure/scales, or if morbidity, reinsurance revised.

### 2.4. Sensitivity when assessing return on capital/profitability

2.4.1. *of EB, can use sensitivity analysis to present effect of departures from chosen parameter values. -test parameters such as: claim inception, recovery,rates of transfer,mort, lapse, non renewals, av claim size (indem),exp, ben, inf, inv, vol, mix,tax *If PDF for param, can derive stats for sensitivity analysis - percentiles, CI, Variance, assess margins, effect of departures.

## 3. 5. Equation of value/formula approach

### 3.1. formula approach to pricing

3.1.1. value of claims

3.1.1.1. *Include PV future claim outgo *Maybe included claims handling expenses due to timing *Standard inflation assumptions, or different if specified in policy type.

3.1.2. value of premiums

3.1.2.1. *value of one unit premium income projected and discounted, allow for lapse, escalation, premium holidays, premium related expenses and commissions.

3.1.3. value of expenses

3.1.3.1. *Project discount, allow for inflation

3.1.4. value of investment income

3.1.4.1. *cost of reserves ignored - key point *Value of investment income would be difference of items being recieved by company during the year against outgo, with the balance being invested, to the year end prior value. *Can allow for with adjustments to discounting factors. cashflow will offset during the year, so investment returns will not be the premium invested, but some of it for a while, and then less.

3.1.5. value of tax and other outgo

3.1.5.1. *Adjust discount rate, or explicit allowance on other items - expenses or profit

3.1.6. value of profit to insurer

3.1.6.1. *alter to meet profit objective e.g. 50% annual premium,

3.1.7. drawbacks of formula approach

3.1.7.1. *Good in its simplicity to estimate required premium. but with computational power, should use more informative approach *Drawbacks: -Timings of events -accumulation of reserves -capital needs not allowed for -net negative cashflow impact -can't inspect premium/claim cashflow -varying assumptions -used fixed discount rate -no allowance for changes in future experience -complex product structures Most drawbacks for long term prods, less worse for short term.

3.1.8. *Principle: income must equal outgo, or exceed, with surplus belonging to suppliers of capital - the unknown to solve this equation is premium *Discount rate can be used to meet profit criteria, can add additional profit margins.

## 4. 7. Multistate modelling

### 4.1. Introduction

4.1.1. *PH can be in different states, each state, different cash flows - IP LTCI - where claim doesn't terminate the policy *Various stages of healthy and claiming: Healthy premium payers, sick in deferred period, claimants after deferred, recovering to premium payers, deaths. *own transition rates - sickness, inception, lapse, mortality, recovery, expiry. *probs may also vary by no of times previously sick, depends on sophistication of model. Actuary needs to balance available data vs sophistication.

### 4.2. Multistate modelling for pricing

4.2.1. *need proportion of lives in each status, using relevant duration based intensities *claims outgo depends on no of lives in benefit cohort, in a given month x average SA *balanced against premiums coming in from premium state plus investment income, less expenses and other outgoings *intensities applied to determine states by months. *Could have hundreds of sub cohorts open at any time - duration sick, category of sickness, previous sickness etc, then age, gender, deferred period, smoker status. *Lack of data, statistics, avoidance of spurious, more straightforward approach used.

### 4.3. multistate modelling for reserving/reporting purposes

4.3.1. *Similar tools as pricing, but assumptions adjusted for purpose of valuation.

## 5. 8. appendix

### 5.1. policy liability model

5.1.1. Projecting forward inforce portfolio of policies. Function of: -EB inforce at start -NB in year -future transitions between states -future mortality/lapse non renewal -Expiry Calculate resns, SCR, total pol cash flow, project assets, profits

### 5.2. expense model

5.2.1. total expected expenses Fixed overheads difficult at policy level, should be global

### 5.3. asset model

### 5.4. consolidation

5.4.1. Compare with supervisory valun compare with previous results compare with simplified model. Last page on CH 11 for diagram

### 5.5. 4 types of models used will differ on basis of which policies are included, focus of output, e.g. profit test focus on annual emergence of profit.

## 6. 1. Use of models

### 6.1. usually projection of balance sheet, revenue account (income statement) Uses of modelling: *costing and reserving for options *Model office - NB proj, EV, SCR, Takeover *Reserves - Stat, management account *Pricing - profit, premium rates

## 7. 2. Objectives and basic features of health insurance models

### 7.1. prime objective

7.1.1. *Enable actuary to give advice so can run health insurer in sound financial way, day to day, checks, controls *judgment used for model choice and MPF *Factors affecting choice of MPF: availablitiy/power of computer,variability of contracts, complexity of contracts, age of company, stoch or det mpf, importance and purpose of investigation, time available, sensitivity of results to more or fewer mps.

### 7.2. basic features

7.2.1. *VARIABLE CRISPS CARD *Health model allow for all CF, nature of contract dependent, premium, ben structure, options to convert, extend, inrease without evidence *CF arising from reserve req or solvency margin maintenance. *cf from different states, transactions between states. CF differ markedly between states i.e healthy paying premium, disabled receiving benefits *CF for interactions, particuarly for assets and liabilities being modelled together. Dynamic - interact. inv strategy in response to changing economic conditions - switching to match assets closer. *ability to use stochastic models and simulation needs to be allowed for. e.g. simulate possible distn of claims outgo. e.g. cost of guarantee, only value by stochastic model.

## 8. 6. Cashflow techniques

### 8.1. Cashflow approach to pricing

8.1.1. the process

8.1.1.1. *profit testing on individual products, determine premium, charging structure, to meet profit reqs *Model points - Rep NB, adapt EB for expected future changes. New prod, similar old prod, combo with marketing info *consider mix, EB should be recent one *proj cf, allow for resns, scr, using base set of assns. Prem, expense (initial, renewal, claims), comm, claim, interest on cf and resn, tax, long term - lapse, prem holidays, ben changes, reins. *UL - Alloc cost, BoS, CoClaims,risk charges, unit charges, FMC, UGR,Surrender *Distinguish between physical CF - expense, comm, tax.. and notional - flows from resns *cost of capital - need to consider return on the policy, but also the assets invested to support the capital. i.e. total return on a policy *investigate for possible negative net CF - want self financing *Discount at RDR (req return of comp, level of stat risk on CF) - cf should be net of tax *can use seperate RDR per cf, but tricky *change premium and/or charges to meet profit criterion. can fine tune the model point to get premium levels *NPV as proportion of initial commission can be criteria. *can reach profit in aggregate - NB mix and vol, so individ model points don't need to meet -groups, bands, average assns applied to cohort. -exposed to mix too *Sensitvity test to meet SH req. *determine premium for all contract variations, apply to all other model points to get full set of premiums. e.g. calculated for 5, 10 15 yrs, now interpolate for in between.

8.1.2. use of the cashflow approach in pricing

8.1.2.1. *widely used, less for PMI over one year (expected cost,plus margins over one year is prem) *May use CF for other techniques - PMI high initial expense, maybe spread over expected renewals, so CF model *Adequacy of prem over longer term, long term profit criterion. renewal assns, premium increase assns - useful if want to limit increases in premium by %.

### 8.2. cashflow approach to assessing profitability

8.2.1. the process

8.2.1.1. *of EB *Full policy data set (if pol by pol basis modelling) *or MPFs to rep EB. Previous EB and modify for NB, gone offs, or regenerate model point process *Check suitability - compare supervisory resns calculated vs published values. *PV CF using RDR *normally RDR less for this than for pricing - risks reduced, NB risks less * total or scale up result.

8.2.2. use of the cashflow approach in assessing profitability

8.2.2.1. *discounted future profits aka PVFP or VIF. *look at different levels, product, class, distn channel, subsidaries *Use in EV calculation -'value of future profit stream from the companies exisiting business together with value of any net assets seperately attributable to shareholders' *EV - sum of existing free assets net of liabs, and future profits expected. Appraisal - include good will, value of future NB. *H&C insurer also study profitability by regular profit testing EB on current pricing basis - show if any repricing or alterations required.

### 8.3. Cashflow approach to assessing return on capital

8.3.1. *can gross up net cashflows for expected NB to assess amount of capital required to write - economic or regulatory basis. Pricing cash flows above. *can add to one off development costs to extent that they haven't been amortised and included in expenses. *Get total capital requirement, can compare to with profits expected to emerge so get expected return on capital. *Similar to one model point pricing described above - but examine a group - use a new business model

### 8.4. Cashflow approach to determining captial requirements

8.4.1. *Full model office for capital required to write NB. *individual model points might be scaled up *Assess impact in captial management terms - reg or econ, if prob, can redesign. looking at business as whole. need to assess intensity of capital for writing: rate of ret, opp cost of cap, financial strength show, exposure to risk if less diversified, statutory sol, weaken resilience, inv freedom, strain