Abstract. We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general securities that pay dividen...

We investigate an optimal portfolio allocation problem between a risky and a risk-free asset, as in [1]. They obtained explicit conditions for path-independence and optimality of allocation strategies when the price of the risky asset follows a geometric Brownian motion with constant asset characteristics. This paper analyzes and extends their results for dynamic investment strategies by allowi...

We present a solution to an optimal stopping game for geometric Brownian motion with gain functions having the form of payoff functions of spread options. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit principle. The derived result can be interpreted as pricing the (perpetual) spread game option in the Bl...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically constructed using the classical finite difference methods. W...

This paper introduces an extension of the balanced augmented empirical likelihood method for estimating simulation models. We analyze its performance empirically using MonteCarlo methods, and demonstrate that our new method increases the flexibility and accuracy of the empirical likelihood approach, while preserving both its limit distribution and its consistency for moment condition models. We...

We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean–reverting Ornstein–Uhlenbeck process. Optimal portfolios and maximum expected log–linear utilities from terminal wealth for informed and uninformed investors are derived. We obtain analogous but more g...

We consider the problem of optimal portfolio selection for a multidimensional geometric Brownian motion model. We look for portfolios that maximise the probability of outperforming a stochastic benchmark. More specifically, we seek to maximise the decay rate of the shortfall probability and (or) to minimise the decay rate of the outperformance probability in the long run. A simple heuristic ena...

We find the optimal investment strategy to minimize the expected time that an individual’s wealth stays below zero, the so-called occupation time. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and one risky asset, with the risky asset’s price process following a geometric Brownian motion. We also consider an extension of th...

For a class of subordinators we investigate the spectrum of the infinitesimal generator of subordinate Brownian motion on a closed manifold. We consider three spectral functions of the generator: the zeta function, the heat trace and the spectral action. Each spectral function explicitly yields both probabilistic and geometric information, the latter through the classical heat invariants. All c...

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process ...