Abstract:
 (1) The expected discounted penalty is a generalized notion of the ruin probability in the insurance literature. This function has been a major concern in the pricing of perpetual financial securities and the Laplace transforms of securities with finite maturity, and examples include option theory and credit risk modelling. In this talk, we will report our recent results related to the expected discounted penalty for Levy processes. This is a joint work with YuTing Chen.
(2) In this talk, we address the exponential process $Y(t):=e^{X(t)c}$(c is a normalizing constant), where X(t) is the stationary diffusion which is defined as the weak solution of meanreverting SDE
$dX(t)=\theta (X(t)\mu )dt+\sqrt{v(X(t))}dB(t),~t\geq 0$
We discuss the expected max increments and the correlation decay of the process Y(t). The main motivation and application are to show that Kahane's Tmartingale scheme in the form of P.~Mannersalo, I.~Norros and R.~Riedi (AAP 2002) can be worked out for the exponential process Y(t). We provide three illustrative examples of OU, CIR, and Beta diffusions.
This talk is based on a joint work of V. Anh (Brisbane, AU) and N. Leonenko (Cardiff, UK), and it will appear in J. Stochastic Anal. Appl.
