Related papers: Convex order for path-dependent derivatives: a dyn…
Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this…
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are…
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for…
We study some properties of the American option price in the stochastic volatility Heston model. We first prove that, if the payoff function is convex and satisfies some regularity assumptions, then the option value function is increasing…
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and…
Within a path integral formalism for non-Gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is…