استراتژی های سرمایه گذاری مطلوب جهت قرارداد شرکت Optimal investment strategies for participating contracts

1. Introduction We study the continuous time portfolio selection problem for insurance companies managing the portfolios supporting participating insurance contracts. Participating contracts are constructed to allow policyholders to share in the profits of the investment portfolio, while simultaneously receiving a guarantee that limits their downside. The policyholders pay premiums to the insurer and the collected premiums are pooled within the insurance company’s general account. The contract payoffs are linked to the performance of this account. The insurance company manages the fund in order to hedge its liabilities, and maximize the performance of its residual share of the portfolio after the liabilities have been paid. The objective of the present paper is to develop optimal asset management strategies for the insurance companies, whereas most of the existing literature focuses either on the pricing aspect of participating contracts or certain characterization of the risk which the insurance companies are exposed to from writing these contracts. For example, Briys and De Varenne [4] derive a closed-form valuation based on an option pricing approach for the participating contract, where the policyholder receives a guaranteed rate of interest (namely point-to-point basis guarantee) and some bonuses determined as a fraction of financial gains at the maturity of the contract. Other work on pricing includes Grosen and Jørgensen [13], Siu [22], and Fard and Siu [9]. The literature that focuses on the characterization of insurance companies’ risk exposure includes Kling et al. [18], Gatzert and Kling [12], and Bernard and Le Courtois [2], among others. Kling et al. [18], and Gatzert and Kling [12] investigate some standard risk measures of the participating contracts known as cliquet-style guarantees, for which the policyholder is credited with a certain rate of return every year. Bernard and Le Courtois [2] study the resulting risk profile of both the insurance company and policyholders under two well-known portfolio insurance strategies (i.e., CPPI and OBPI). Earlier work on asset and liability management for participating contracts has often focused on the problem in discrete time with a finite scenario set. The advantage of this setting is that it allows one to consider more complex and flexible contract structures. Its disadvantages include a lack of closed form solutions, and computational challenges in generating and working with scenario trees. Examples include Consiglio et al. [7] and Consiglio et al. [6], both of which employ scenario optimization in discrete time to analyze problems faced by insurers offering participating contracts with minimum guarantees.