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Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…

We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…

When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the…

We consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid risky asset (no transaction…

Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…

A financial system is represented by a network, where nodes correspond to banks, and directed labeled edges correspond to debt contracts between banks. Once a payment schedule has been defined, where we assume that a bank cannot refuse a…

A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process.…

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…

We consider a seller who offers services to a buyer with multi-unit demand. Prior to the realization of demand, the buyer receives a noisy signal of their future demand, and the seller can design contracts based on the reported value of…

It is well-known that Excess-of-Loss reinsurance has more marketability than Stop-Loss reinsurance, though Stop-Loss reinsurance is the most prominent setting discussed in the optimal (re)insurance design literature. We point out that…

I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…

We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently…

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and…

Volume imbalance in a limit order book is often considered as a reliable indicator for predicting future price moves. In this work, we seek to analyse the nuances of the relationship between prices and volume imbalance. To this end, we…

The steadily high demand for cash contributes to the expansion of the network of Bank payment terminals. To optimize the amount of cash in payment terminals, it is necessary to minimize the cost of servicing them and ensure that there are…

When a loan is approved for a person or company, the bank is subject to \emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a bank will require some form of \emph{security}, which will be collected if the lender…

We consider a periodic-review, fixed-lifetime perishable inventory control problem where demand is a general stochastic process. The optimal solution for this problem is intractable due to "curse of dimensionality". In this paper, we first…

A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently…

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant…

Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by…