2013 | Zastosowanie metod ilościowych w zarządzaniu ryzykiem w działalności inwestycyjnej | 115--139
Stochastic dynamic optimization model of insurance pricing under the assumption of linear demand
We have found the optimal price and investment strategy for an insurer using the stochastic optimal control theory. We establish a pricing model with the assumptions that the price, the investment and the claim loss rate are stochastic processes, and we also assume that the insurance price is a linear function of the demand. The objective of our model is to maximize the expected utility of terminal wealth of the insurer. We establish a HJB equation and obtain the optimal solutions of dynamic insurance price and investment strategy. We also study the sensitivity of the models by varying the parameters. The results in this paper also shows that the return rate and volatility of investment will affect the insurance price in the cases that the slope of linear insurance demand function is relatively larger and their influence will decrease with the decrease of the value of the slope and has no effect when the slope is small enough. This work could have possible applications for insurance firm, which would like to seek optimal dynamic management strategy, and using a model similar to ours as a permanent enterprise risk management tool. It should be noted that regulatory developments, for example Solvency II in the European Union, encourage or even require such integrated risk management approach. Let us also note that our model can be further extended by considering more complex structure of risks, e.g., multiple risky asset classes, and relaxing our rather restrictive assumptions about the market price process, utility of wealth, and demand for insurance. (fragment tekstu)
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