数理金融

A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The…

The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by…

The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the…

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation…

Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…

The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimization problems for functions of…

In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise…

We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…

In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it…

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal…

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised…

Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An…

We develop a version of the fundamental theorem of asset pricing for discrete-time markets with proportional transaction costs and model uncertainty. A robust notion of no-arbitrage of the second kind is defined and shown to be equivalent…

This paper includes an original self contained proof of well-posedness of an initial-boundary value problem involving a non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. We call…

This paper focuses on the stability of the non-arbitrage condition in discrete time market models when some unknown information $\tau$ is partially/fully incorporated into the market. Our main conclusions are twofold. On the one hand, for a…

In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected…

In this paper, we assume an insure is allowed to purchase proportional reinsurance and can invest his or her wealth into the financial market where a savings account, stocks and bonds are available. Different from classical optimal…

We obtain a first order extension of the large deviation estimates in the G\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order…

This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…

We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic…