LiFePO4 nanocrystals were synthesized in various polyol media without any further post-heat treatment. The LiFePO4 samples synthesized using three different polyol media namely, diethylene glycol (DEG), triethylene glycol (TEG), and tetraethylene glycol (TTEG), exhibited plate and rod-shaped...

We show that the mutual fund theorems of Merton [1971. Journal of Economic Theory 3, 373-413] extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random...

In this paper, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.

We find the optimal investment strategy for an individual who seeks to minimize one of four objectives: (1) the probability that his/her wealth reaches a specified ruin level before death, (2) the probability that his/her wealth reaches that level at death, (3) the expectation of how low his/her...

For $\alpha \in (1, 2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit...

This paper studies the utility maximization problem on the terminal wealth with both random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system...

In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been discovered is quite nonintuitive. By answering several...

We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle $L$ and the upper obstacle $U$ of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by...