Julie Thøgersen has received the 1st prize among the speakers at the workshop Perspectives on Actuarial Risk in Talks of Young Researchers held in Ascona, Switzerland January 8-13.
The prize is participation in the conference Insurance: Mathematics and Economics to be held in Vienna in July, with all expenses covered.
Her winning talk was entitled:Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics.
Abstrakt: An insurance company offers an insurance contract $(p,K)$, consisting of a premium $p$ and a~deductible $K$. In this paper, we consider the problem of choosing the premium optimally as a function of the deductible. The insurance company is facing a market of $N$ customers, each characterized by their personal claim frequency, $\alpha$, and risk aversion, $\beta$. When a customer is offered an insurance contract, she/he will, based on these characteristics, choose whether or not to insure. The~decision process of the customer is analyzed in detail. Since the customer characteristics are unknown to the company, it models them as i.i.d. random variables; $A_1, \ldots, A_N$ for the claim frequencies and $B_1, \ldots, B_N$ for the risk aversions. Depending on the distributions of $A_i$ and $B_i$, expressions for the portfolio size $n(p;K) \in [0,N]$ and average claim frequency $\alpha(p;K)$ in the portfolio are obtained. Knowing these, the company can choose the premium optimally, mainly by minimizing the ruin probability.