PENENTUAN CADANGAN MANFAAT PADA ASURANSI KONTRAK DENGAN MEMAKSIMALKAN EKSPEKTASI UTILITAS EKSPONENSIAL; DETERMINING BENEFIT RESERVES OF INSURANCE CONTRACTS WITH MAXIMIZING THE EXPECTED EXPONENTIAL UTILITY

ALFIANA, KHOIROH, Adhitya Ronnie Effendie

2016 | Disertasi | FMIPA

In this paper, we discuss an optimal strategy investment problem of an insurance company. Portofolio investments consist a risky asset and money market, which the risky asset modeled as diffusion presses follows Brown motion geometry. The insurance company as risk averter with preferences are exponential. When the insurer preferences are exponential to give an explicit form of the optimal strategy. In order to solve optimization problem, we use Hamilton-Jacobi-Bellman equation. And then, we estimate an explicit form of indifference premium of insurance contracts under optimal strategy with maximizing expected exponential utility and benefit reserves for that indifference premium, which collective risk model follows compound Poisson process.

Kata Kunci : Optimal strategy, Hamilton-Jacobi-Bellman equation, geometric Brown motion, indifference premium, benefit reserve, exponential utility function.