Cash Accumulation Strategy based on Optimal Replication of Random Claims with Ordinary Integrals

TL;DR

This paper introduces a numerical model for designing cash accumulation strategies by exactly replicating stochastic asset price processes at a future time using ordinary integrals, applicable to various asset combinations.

Contribution

It proposes a novel approach to cash accumulation by matching stochastic processes with ordinary integrals, enabling precise future asset value targeting.

Findings

Model effectively matches Wiener Process at terminal time

Application to single and multiple assets demonstrated

Efficiency varies with model parameters

Abstract

This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary integrals this Wiener Process will be exactly matched at a preset terminal time. Three applications of the model are presented: accumulating cash for a single asset, for set of different assets, and for a proportion of the excess achieved by a certain asset. Furthermore, an analysis of the efficiency of the model as function of different parameters is performed.