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This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier…
We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic…
We consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general…
We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical…
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use…
This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real…
We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these…
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write…
We consider separable nonconvex optimization problems under affine constraints. For these problems, the Shapley-Folkman theorem provides an upper bound on the duality gap as a function of the nonconvexity of the objective functions, but…
We show a close connection between structural hardness for $k$-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite…
In this paper, we propose a stochastic version of the classical Tseng's forward-backward-forward method with inertial term for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued monotone operator…
In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with…
We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market,…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
We study the valuation of an American put option with a random time horizon given by the last exit time of the underlying asset from a fixed level. Since this random time is not a stopping time, the problem falls outside the classical…