Tempting to formulate the long-term investment strategy for investors who dynamically adjust her portfolio over her lifetime, we are interested to optimize the end-of-period terminal wealth using Bellman Principles. We designed the portfolio to be replete with risky asset and risk-less...

In this study, the scheme of Dynamic Portfolio consisted of three assets (Stock, Bond and Money account) were generated for investor who want to maximize the discounted expected utility for terminal wealth along finite time horizon in complete market in which inflation rate, interest rate and...

Motivated by observation that seminal work of Samuelson obtaining optimal investment on risky asset which was independent of time and wealth process, in this paper we were replacing the source of uncertainty in the risky asset by binomial process in order to improve the model. Risky asset is...

Motivated by problems in mathematical finance and insurance, this paper discusses optimal stopping problem in general setting. It considers discounted running cost and stopping cost in addition to terminal gain in the objective function, subject to be optimized over finite-time period. The...

Given a spectrally-negative Lévy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever the observed value is above it. We also consider the versions with additional classical reflection above and/or...

We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type.

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Lévy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide...

We study a zero-sum game where the evolution of a spectrally one-sided Lévy process is modified by a singular controller and is terminated by the stopper. The singular controller minimizes the expected values of running, controlling and terminal costs while the stopper maximizes them. Using...

Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of...