Quantitative Finance Research Centre

Quantitative Finance Research Centre Quantitative F Inance Research Centre

Time-Inconsistent Stochastic Linear-Quadratic Control: Characterization and Uniqueness of Equilibrium

In this paper, we continue our study on a general time-inconsistent stochastic linear–quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward– backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the ...

Optimal Stopping under Probability Distortion∗

We formulate an optimal stopping problem where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can t...

Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomi...

Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre

In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito’s lemma. An integral expression for the general solution of the PDE is presented b...

Greed, Leverage, and Potential Losses: A Prospect Theory Perspective

Partly motivated by a deeper understanding of the role human greed has played in the current financial crisis, this paper quantifies the notion of greed, and explores its connection with leverage and potential losses, in the context of a continuoustime behavioral portfolio choice model under (cumulative) prospect theory. We We are grateful for comments from seminar and conference participants a...