Dear Colleagues and Students,
You are invited to a series of seminars on Financial Mathematics in Spring 2019.
The third seminar is on 30 April 2019, Tuesday. Here is the detailed information.
Title: Ruin problems with risky investments
Speaker: Yuri Kabanov, University of Franche-Comté, France, and Lomonosov Moscow State University, Russia
Date : 30 April 2019, Tuesday
We are interested in the asymptotic of the ruin probability for a process describing the evolution of the capital reserve of an insurance company investing its capital reserve in a risky asset with the price given by a geometric Lévy process, e.g. a geometric Brownian motion. Mathematically, the dynamics of reserve can be described by a generalized Ornstein–Uhlenbeck process. To the moment there are two methods of study: based on integro-differential equations for ruin probabilities and the implicit renewal theory. As an example for the company selling annuities, the business process has upward jumps. For the investments, we suppose that the cumulant-generating function H(q) = ln E e^-qV_1 of the increment of log price process V admits a root beta > 0 at which H is continuous while the business activity process is not a subordinator. We show that the ruin probability has the exact asymptotic Cu^−beta as u->infty. We also discuss conditions under which the ruin happens with probability one.
Bio: Yuri Kabanov is a Professor of Mathematics at the University of Franche-Comté in France as well as at Lomonosov Moscow State University in Russia. He held positions at the Central Economics and Mathematical Institute of the Russian Academy of Sciences, Higher School of Economics, International Laboratory of Quantitative Finance as well as at Bilkent University during 1993-1994. He holds a PhD in Mathematics from Steklov Mathematical Institute of the USSR Academy of Sciences. Yuri Kabanov’s research interests cover a wide range of subjects including point processes, stochastic integration, stochastic control, arbitrage theory, markets with transaction costs and systemic risk. He has had editorial positions at journals including Finance and Stochastics, Annals of Applied Probability, Probability Theory and its Applications, Informatics and Applications.