2021/01/01 by Mahan Tahvildari, Tahvildari, Mahan
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Risk Management in Financial Firms #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2101.00251
openalex publication_date 2021/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the hedging and valuation of European and American claims on a\nnon-traded asset Y, when a traded stock S is available for hedging, with\nS and Y following correlated geometric Brownian motions. This is an\nincomplete market, often called a basis risk model. The market agent's risk\npreferences are modelled using a so-called forward performance process (forward\nutility), which is a time-decreasing utility of exponential type. Moreover, the\nmarket agent (investor) does not know with certainty the values of the asset\nprice drifts. This market setting with drift parameter uncertainty is the\npartial information scenario. We discuss the stochastic control problem\nobtained by setting up the hedging portfolio and derive the optimal hedging\nstrategy. Furthermore, a (dual) forward indifference price representation of\nthe claim and its PDE are obtained. With these results, the residual risk\nprocess representing the basis risk (hedging error), pay-off decompositions and\nasymptotic expansions of the indifference price in the European case are\nderived. We develop the analogous stochastic control and stopping problem with\nan American claim and obtain the corresponding forward indifference price\nvaluation formula.\n