Eberlein, Kallsen and Kristen (2003) argued that the VIX index is a good way to devolatize SPX returns. Adopting this approach we construct a risk neutral model for SPX returns as a variance gamma process scaled by the VIX. We model the risk neutral evolution of the squared VIX as a mean...

In this paper we explore a novel way to combine the dynamic notion of time-consistency with the static notion of quantile-based coherent risk-measure or spectral risk measure, of which Expected Shortfall is a prime example. We introduce a class of dynamic risk measures in terms of a certain...

The paper provides a new hedging methodology permitting systematic hedging choices with wide applications. Dynamic concave bid price, and convex ask price functionals from the recent literature are employed to construct new hedging strategies termed dynamic conic hedging. The primary focus of...

We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a...

Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro–differential equations that are solved numerically for the three...

We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance...

We derive the exact asymptotics of P(supu<=tX(u)>x) if x and t tend to infinity with x/t constant, for a general Lévy process X that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of Höglund [Höglund, T., 1990. An asymptotic expression for...</=tx(u)>