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We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit…

We apply rough-path theory to study the discrete-time gamma-hedging strategy. We show that if a trader knows that the market price of a set of European options will be given by a diffusive pricing model, then the discrete-time gamma-hedging…

This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when…

There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study…

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…

We consider the problem of ESO valuation in continuous time. In particular, we consider models that assume that an appropriate random time serves as a proxy for anything that causes the ESO's holder to exercise the option early, namely,…

We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…

This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…

We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…

We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…

Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…

The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely…

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…

In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…

We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…