This paper considers a utility maximization and optimal asset allocation problem in the presence of stochastic endowment that cannot be fully hedged through trading financial market. We rely on dynamic programming approach to solve optimization problem. The properties value function, particularly homogeneity, are used reduce HJB equation by one dimension. Furthermore, strategy is derived, its a...

Many highly reliable products are designed to function for years without failure. For such systems accelerated degradation testing may provide significance information about the reliability properties of system. In this paper, we propose c-optimality criterion obtaining optimal designs constant-stress tests where path follow a linear mixed effects model. The present work is mainly concerned wit...

We consider two dimensional Grushin Schr\"odinger equation posed on a finite cylinder $\Omega=(-1,1)_x\times \T_y$ with Dirichlet boundary condition. obtain the sharp observability by any horizontal strip, optimal time $T_*>0$ depending size of strip. Consequently, we prove exact controllability for equation. By exploiting concentration eigenfunctions harmonic oscillator at $x=0$, also show tha...