In this thesis, we look into two important issues that involve the interplay between insurance and finance, namely the pricing of insurance-linked securities (ILS) and the liquidation risk in insurance under contemporary regulatory frameworks.
First, we employ the utility indifference and risk-neutral pricing approaches to price ILS. For the former, we extend the utility indifference pricing approach widely used in one-period models to a multi-period case with intermediate payments by working with time-$0$ equivalent values and solving, through backward induction, a multi-period optimization problem. We offer insights into the issues regarding coherence and time consistency of the ask and bid indifference prices obtained. For the latter, we focus on three desirable properties of a pricing measure in an arbitrage free and incomplete market, namely, equivalence, structure preserving, and amplifying unfavorable events. We also propose a downside risk process which enables us to quantify the riskiness of an ILS and to characterize the property of amplifying unfavorable events under our framework.
Second, we quantify the rehabilitation proceeding in insurance, which is akin to Chapter 11 reorganization of the U.S. Bankruptcy Code, and we conduct a probabilistic analysis of the liquidation risk of an insurance company having the option of rehabilitation. In doing so, we construct a three-barrier model to describe the solvent and insolvent states in which the surplus process follows either different time-homogeneous diffusions or different double exponential jump-diffusions. We derive analytical expressions for the liquidation probability and the moment generating function of the liquidation time with a fixed or an independent exponentially distributed grace period.