Keywords

Insurance, Investments, Optimal Control, Ruin Probability

Abstract

Insurance is that insurer collects premiums from insured and reimburses claims. If the premiums collected are not enough to pay claims, insurance company will go bankrupt. Therefore, insurer may need to consider ruin probability of insurance to avoid bankruptcy. In this article, we assume that insurer invests premiums in both risky and risk-free assets with some allocated restrictions. We will try to find the optimal investment proportion by maximizing expected general utility function of surplus process corresponding to the ruin probability. We will prove that the optimal investment proportion has ”bang bang” characteristic under some conditions.

Moreover, in traditional term life insurance, insurer will pay a fixed death benefit to beneficiary if insured dies before or at the end of the term. If insured survives at the end of the term, both beneficiary and insured will get nothing. Based on current term life insurances, we set up an extended term life insurance with some new features. Premiums will be invested in both risky and risk-free assets. If insured dies before or at the maturity date, beneficiary can get the fixed death benefit. Moreover, if insured survives, insured can get the survival benefit which is part of the return from the investments. By having a fixed death benefit and an investment sharing survival benefit, insured or beneficiary can get something no matter death or survival of insured. However, insurer may confront some investment risk in this insurance, so we will find a suitable range of premium payments and use optimal control theory to find the optimal investment strategy to see the expected survival benefit.

Completion Date

2025

Semester

Summer

Committee Chair

Yong, Jiongmin

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Format

PDF

Identifier

DP0029580

Language

English

Document Type

Thesis

Campus Location

Orlando (Main) Campus

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