Two insurance/finance risk management problems

Abstract

The thesis contains two parts that study two different risk management problems in the insurance and financial markets.

The first part of the thesis is about a novel extension of the concept of Parisian ruin. Ruin is said to occur when the time that the surplus process cumulatively stays under zero exceeds a certain threshold d (the delay). Four ultimate and finite-time ruin probabilities are derived: (1) ultimate cumulative Parisian ruin with (a) deterministic delay or (b) Erlang delay; (2) cumulative Parisian ruin within an Erlang time horizon with (a) deterministic delay or (b) Erlang delay. Then numerical examples are presented to investigate the effect of Erlangization.

The second part we investigate the effect of transparent traders' (interpreted as mutual funds) ambiguity to the positions of opaque traders (interpreted as hedge funds). The positions other than the equity market investment of a hedge fund is summarized in the extra investment opportunities (EIOs). The decision making of transparent traders is modeled by the smooth utility model of ambiguity. The equilibrium result reveals that they have a persistent superior performance than mutual funds. Then, after endogenizing the trader distribution, we analyze how regulations pertaining to hedge funds (or other market participants without enough disclosure requirements) affect the distributions of traders, equity premium, and welfare level of the whole market.