For wide classes of put-like and call-like perpetual options under Levy processes satisfying the (ACP)-property, the optimal exercise price and rational option price are found. The results are formulated in terms of resolvent operators of the supremum and infimum processes, which are natural...

In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial, model-dependent payoff structures. We derive new integral...

We describe a fast new method for the market implied calibration of the Heston (1993) model for equity, based on an improved version of the parabolic pricing algorithm of Levendorskii (2012). This pricing method, when used in the calibration, is much faster and more accurate, and better...

For wide classes of payoff functions and Lévy processes, we solve perpetual restricted optimal stopping problems, when one exercise region is exogenously given (barrier like feature), and the other is chosen to optimize the option value, and straddle-like perpetual options, when the optimal...

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of L'evy models and the Heston model. In the present paper we construct efficient conformal deformations of the contours of integration in the...

In the standard optimal stopping problems, actions are artificially restricted to the moments of observations of costs or benefits. In the standard experimentation and learning models based on two-armed Poisson bandits, it is possible to take an action between two sequential observations. The...

We generalize the Piterbarg (2010) model to include 1) bilateral default risk as in Burgard and Kjaer (2012), and 2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options...

A backward induction procedure for pricing arithmetic Asian options in Levy models is realized in the dual space. Each step of the procedure is the composition of a multiplication operators by an explicitly given function, and the convolution operator ${\cal H}_\Ga$, which belongs to a class of...

An ambiguity averse decision-maker contemplates investment of a fixed size capital into a project with a stochastic profit stream under the Knightian uncertainty. Multiple priors are modeled as a "cloud" of diffusion processes with embedded compound Poisson jumps. The "cloud" contains the...

We study a stochastic version of Fudenberg -- Tirole's preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader's...