Research On Measuring Economic Capital For Insurance Risk

Being different from other financial institutions, insurance companies receive premi-ums at the very beginning and carry out claims outgo afterwards. Thus insurers have to keep reserves in order to ensure solvency. For a non-life insurance company, the valuation mostly depends on the historical claim data and actuary's empirical judgement due to lack of industry data and well developed model. It can underestimate the ultimate loss for a policy year because of the deficiency of pricing and reserving and makes the company unable to pay for a future claim. As a result, company should keep certain level of capital to cover such risks (called insurance risk), that is economic capital. The article tries to model the insurance risk and calculate its economic capital at a given level.Chapter 1 introduces the background and researches that have been done before. Chapter 2 concerns about the dependence structure while aggregating risks. Chapter 3 analyze concepts and methodologies about the reserve valuation for Property and Casualty (P/C) insurers to define pricing risk and reserving risk. In chapter 4, the ultimate loss random variable is used to quantify the insurance risk. With underwriting circle as time horizon, for each policy year, the sum of the unearned loss cost and the current estimate of accident years'ultimate losses form a new estimate of the ultimate losses at each evaluation age. After that, Estimates errors are defined and assumed to be lognormal. The distribution for the ultimate loss random variable can then be derived. With loss model built, the economic capital for insurance risk is determined using VaR. Chapter 5 test the constructed model using the data of motor and marine insurance.The major contribution of this article is constructing an economic capital model us-ing the same data segments, same development factors and definition with the reserving process, which makes the model convenient and possible to be carried out for the reserv-ing department. Meanwhile, when extending the model to multi-line business, copula is introduced to evaluate the dependence structure for measuring the diversification of risk aggregation. Theoretically, copula makes the model able to capture all possible depen-dence structures between different insurance risks and thus measure the overall economic capital more accurate and realistic.