Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around the line of integration in the complex plane.The Fourier transform techniques reduces calculation of probability distributions and option...

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...

Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of L'evy models, the Heston model and other affine models. Similar deformations were used in one-factor L'evy models to...

A general framework for pricing of real options in continuous time for wide classes of payoff streams that are monotone functions of a Levy process is provided. Exercise rules are formulated in terms of statistics of record-setting low payoffs and can be viewed as an extension of Bernanke's bad...

We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical...

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Gaussian model with the same instantaneous variance. Numerical results are produced to show that for typical parameters values, the relative error of the Gaussian...

The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities exhibit exponential decay, and the rate of decay is large. This leads to asymptotic...

We solve the pricing problem for perpetual American puts and calls on dividend-paying assets. The dependence of a dividend process on the underlying stochastic factor is fairly general: any non-decreasing function is admissible. The stochastic factor follows a Levy process. This specification...

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...