Maxim Bichuch

Utility Maximization Trading Two Futures with Transaction Costs

An agent invests in two types of futures contracts, whose prices are possibly correlated arithmetic Brownian motions, and invests in a money market account with a constant interest rate. The agent pays a transaction cost for trading in futures proportional to the size of the trade. She also receives utility from consumption. The agent maximizes expected infinite-horizon discounted utility from consumption. We determine the first two terms in the asymptotic expansion of the value function in the transaction cost parameter around the known value function for the case of zero transaction cost. The method of solution when the futures are uncorrelated follows a method used previously to obtain the analogous result for one risky asset. However, when the futures are correlated, a new methodology must be developed. It is suspected in this case that the value function is not twice continuously differentiable, and this prevents application of the former methodology.

Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment

We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of

Portfolio Optimization Under Convex Incentive Schemes

\varepsilon^{\frac{1}{3}}

Arbitrage-Free XVA

in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of

Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis

\varepsilon^{\frac{2}{3}}

Arbitrage-Free Pricing of XVA - Part I: Framework and Explicit Examples

. In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims.

Investing with Liquid and Illiquid Assets

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function

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g

Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon

of the terminal wealth. The managers own utility function

Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs

U