Related papers: Closed-form approximations in multi-asset market m…
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
We study the analyticity of the value function in optimal investment with expected utility from terminal wealth and the relation to stochastically dominant financial models. We identify both a class of utilities and a class of…
This note provides upper bounds on the number of operations required to compute by value iterations a nearly optimal policy for an infinite-horizon discounted Markov decision process with a finite number of states and actions. For a given…
We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have…
Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have…
The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is…
In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of…
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of…
These notes form part of a joint research project on the logic of fields with many valuations, connected by a product formula. We define such structures and name them {\em globally valued fields} (GVFs). This text aims primarily at a proof…
The Efficient Market Hypothesis has been a staple of economics research for decades. In particular, weak-form market efficiency -- the notion that past prices cannot predict future performance -- is strongly supported by econometric…
One of the key approaches to save samples in reinforcement learning (RL) is to use knowledge from an approximate model such as its simulator. However, how much does an approximate model help to learn a near-optimal policy of the true…