International Journal of Theoretical and Applied Finance

How should one construct a portfolio from multiple mean-reverting assets? Should one add an asset to a portfolio even if the asset has zero mean reversion? We consider a position management problem for an agent trading multiple mean-reverting assets. We solve an optimal control problem for an agent with power utility, and present an explicit solution for several important special cases and a semi-explicit solution for the general case. The near-explicit nature of the solution allows us to study the effects of parameter misspecification, and derive a number of properties of the optimal solution.

In this paper, we introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability of exploding scenarios, arising in particular in the market-consistent valuation of long-term guarantees. To this end, we prove existence and uniqueness of the corresponding MF-LMM and investigate its practical aspects, including Black’s formula. Moreover, we present an extensive numerical analysis of the MF-LMM. The corresponding Monte Carlo method is based on a suitable interacting particle system which approximates the underlying mean-field equation.

In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for the investor, which also implies that there can be no crash at all. For the modeling of the parameter uncertainty, we choose a general definition of the sets of possible drift and volatility parameters, conditioned by the solution of an optimization problem. In addition, these sets may be different in the pre-crash and post-crash market. We solve this portfolio problem and then consider two particular examples with box uncertainty and ellipsoidal drift ambiguity.

In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.

We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on prices, the large trader may also be tempted to minimize the payoff of the derivative by manipulating the underlying asset. Since the option holders have the right to exercise the option at any time before expiry, we consider a robust optimization problem for the large trader, in which the underlying uncertainty is the exercise time. It is shown that the solution of this optimization problem can be described as the solution of a double obstacle variational inequality. The optimal strategy for the large trader and the worst-case exercise time for the option holder are obtained explicitly in terms of the value function. We conclude with a sensitivity analysis in which we compare the timing and size of trades by the large trader as well as the exercise region for the options holders for different levels of liquidity, and identify situations that may lead to potential price manipulation.