AbstractsBusiness Management & Administration

Introduction An important issue in actuarial theory is to study the ruin probability of an in- surance company when the management has the possibility of investing in the financial market. Azcue and Muler(2009) studies the problem of finding the op- timal dynamic investment strategy which minimizes the ruin probability under infinite time horizon [1]. It is assumed that the financial market follows a classic Black-Scholes model consisting of one risk-free asset (bond) and one risky asset (stock). The insurance claims follow ordinary models in general insurance. One problem with the Azcue and Muler solution is that insurance companies do not decide financial strategies for infinite time periods. Normally 5 to 15 years will be more than enough. This thesis tries to find optimal dynamic strategies for these more realistic time perspectives. The same model as in Azcue and Muler(2009) will be used. I will solve this problem recursively with the Bellman equation (known as a dynamic programming equation). Dynamic programming breaks the optimization problem into two sub problems, making a initial decision based on the initial capital and making decisions for the rest of the time period where we only have a probability of what the capital will be. The probability distribution for the balance of an insurance company is difficult to calculate analytically, I will therefore use Monte-Carlo simulations to approximate the probability distribution. One problem is that since we are dealing with a recur- sive method, there can be to many simulations for the computer to handle. Chapter 2 will introduce the models that are used and show a simple exact cal- culation to a simplified problem. Chapter 3 will show the ruin probability and the optimal strategy with fixed weights. The theory on dynamic programming, and how we solve our problem with the Bellman equation on the computer are