We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we...

In this paper, we prove a maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem, a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits...

We study stochastic forced oscillations of a mass-spring system with time-dependent, stochastic damping. The main purpose is to analyze the effect of the time-dependent damping. The oscillations are governed by the second-order stochastic differential equation , where x denotes the motion, Wt...

In this paper, we first study the problem of minimal hedging for an insider trader in incomplete markets. We use the forward integral in order to model the insider portfolio and consider a general larger filtration. We characterize the optimal strategy in terms of a martingale condition. In the...

We consider a financial market driven by a Levy process with filtration  [image omitted]. An insider in this market is an agent who has access to more information than an honest trader. Mathematically, this is modelled by allowing a strategy of an insider to be adapted to a bigger filtration...

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+[sigma](t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in...