Related papers: On discrete time hedging in d-dimensional option p…

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…

Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…

A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both…

We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…

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…

Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…

This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on…

We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…

In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price…

We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…

We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$,…

Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…

First, we consider the problem of hedging in complete binomial models. Using the discrete-time F\"ollmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in…

This paper deals with the filtering problem for a class of discrete time stochastic volatility models in which the disturbances have rational probability density functions. This includes the Cauchy distributions and Student t-distributions…

In this paper we propose a new method of estimation for discrete choice demand models when individual level data are available. The method employs a two-step procedure. Step 1 predicts the choice probabilities as functions of the observed…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this…