We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems...

We investigate whether a model with time-varying probability of economic disaster can explain prices of collateralized debt obligations. We focus on senior tranches of the CDX, an index of credit default swaps on investment grade firms. These assets do not incur losses until a large fraction of...

In this paper we propose a novel flexible framework based on time changed Lévy process for the joint evolution of stock log-returns and their volatility with the aim of analysing which risk factors and which distribution features provide a robust calibration, repricing and hedging performance....

We survey several models of liquidity and liquidity related problems such as optimal execution of a large order, hedging and super-hedging options for a large trader, utility maximization in illiquid markets and price impact models with price manipulation strategies

This paper reconsiders the predictions of the standard option pricing models in the context of incomplete markets. We relax the completeness assumption of the Black-Scholes (1973) model and as an immediate consequence we can no longer construct a replicating portfolio to price the option....

We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with the continuation region determined by an increasing continuous boundary...

In this paper, we present a new approach to measure the returns of private equity investments based on a stochastic model of the dynamics of a private equity fund. Our stochastic model of a private equity fund consists of two independent stages: the stochastic model of the capital drawdowns and...

This paper presents a unified framework for examining the general equilibrium effects of transactions costs and trading constraints on security market trades and prices. The model uses a discrete time/state framework and Kuhn- Tucker theory to characterize the optimal decisions of consumers and...

In this paper, we present a new approach to measure the returns of private equity investments based on a stochastic model of the dynamics of a private equity fund. Our stochastic model of a private equity fund consists of two independent stages: the stochastic model of the capital drawdowns and...