Jin Ma (Purdue University, Mathematics)

An emerging trend in actuarial mathematics has been to infuse modern theory of mathematical finance into the study of actuarial problems. Thus a general insurance risk model today often involves at least two types of uncertainties: one from traditional claims, and the other from investment returns. In this talk I will describe how such a trend will give rise to interesting problems in stochastic analysis and stochastic finance.

Starting from the simplest classical Cremer-Lundberg model, and with three major problems in mind: ruin probability, optimization with reinsurance, and equity-linked insurance pricing, we show how martingale theory, large deviation, stochastic control theory, backward stochastic differential equations (with jumps), nonlinear Feynman-Kac formula, and even hot finance topics such as credit risk, indifference pricing, etc., will all find their places in this relatively ``ancient" subject.