Extreme Value Theory in the Study of Ruin with Risky Investments

• Activity Number: 443
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Qihe Tang*+ and Raluca Vernic and Zhongyi Yuan
• Companies: University of Iowa and Ovidius University of Constanta and University of Iowa
• Keywords: Asymptotics ; Finite-time ruin probability ; Max-domain of attraction ; Multivariate regular variation ; Optimal investment strategy ; Subexponential distribution

Abstract

Consider a discrete-time insurance risk model in which periodic claim amounts and premium incomes form a sequence of independent and identically distributed random pairs, each with dependent components. The insurer is allowed to invest a constant fraction of his/her wealth in a risky stock and keep the remaining wealth in a risk-free bond. For subexponential periodic net losses and arbitrarily dependent stock return rates, we derive a general exact asymptotic formula for the finite-time ruin probability. If the loss distribution also belongs to the max-domain of attraction of the Fr\'{e}chet or Gumbel distribution and the return rates jointly follow Sarmanov's distribution, the obtained general formula is further refined to be completely transparent. As an application, we approximate the value of the fraction invested to the risky stock that maximizes the expected terminal wealth of the insurer subject to a constraint on the ruin probability.