Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.

Description: Introduction to Actuarial Considerations in Insurance Mergers and Acquisitions, M-FI03-1.

Description: New tools for managing insurance risk have particularly emerged in the 1980s and 1990s, usually with roots in the financial markets. A strong motivating factor has been the record number of natural catastrophes and their impact in insured losses. New organization or joint ventures have been created to meet this demand. From Securitization of Insurance Risk: The 1995 Bowles Symposium, M-FI97-1.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].

Description: The amount of 1 [i.e., the amount that $ 1 is worth after 1 year] for an account earning a nominal interest r compounded n times annually is Pn[r,t], where t = [t1, . . . ,tn]. Note that Pn[r,t] is a polynomial in r of degree n. Now suppose that the n compounding periods have lengths T1, . . . ,Tn chosen at random. What can we say about Pn[r , T] , where T=[T1, . . . , Tn]? This depends of course on what is meant by choosing random lengths and we will consider two different natural possibilities that give rise to different answers to this question.

Description: Given a financial transaction we are often interested in the number of internal rates of return [yield rates] and their location. From an actuarial point of view, the fundamental question is to identify those transactions with a single yield rate, or a single rate in some interval such as the positive reals. In this paper we are concerned with this counting problem. We survey various results concerning this problem, and provide a unifying approach together with some new insights.

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: This paper explores Indian futures and options market as a market for hedging by equity holders. The authors have tried to examine optimal hedge ratio and hedge efficiency, and to provide empirical evidence from India.

Description: Much of the push for ERM has come from regulators and rating agencies, but it is being applied in internal company decision-making as well. This paper reviews the progress made and the needs still outstanding in two key areas of application: optimal capital level for an insurer and risk-adjusted profitability of business units. The basic conclusion is that progress has been made in these areas, but more is needed. Building models is not emphasized—it will be assumed that a state-of-the art model is available. The emphasis is on using such models in decision-making.

Description: The paper o ers a simple framework for ranking the common reinsurance struc- tures in practice with the theory of stochastic orders. The basic idea is to slice the space of reinsurance structures into groups by expected loss cost to facilitate the comparisons within the group and between groups. Given the standard risk aversion assumption in economics, a spectrum of reinsurance structures with the same expected loss cost can be compared analytically with one another and sequenced based on their risk coverages under the convex order. The paper then expands the dimension of the comparison to groups of reinsurance structures with di erent expected loss costs, which can be ranked under the increasing convex order and the usual stochastic order. As such, the paper maps out the ordering for the entire space of reinsurance structures and presents it in a ma- trix format for quick reference. The implication