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Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to…
This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is…
We study buyer-optimal procurement mechanisms when quality is contractible. When some costs are borne by every participant of a procurement auction regardless of winning, the classic analysis should be amended. We show that an optimal…
Agents that plan and act in the real world must deal with the fact that time passes as they are planning. When timing is tight, there may be insufficient time to complete the search for a plan before it is time to act. By commencing…
Executing smart contracts is a compute and storage-intensive task, which currently dominates modern blockchain's performance. Given that computers are becoming increasingly multicore, concurrency is an attractive approach to improve…
We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before…
We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…
We study the problem of optimal execution of a trading order under Volume Weighted Average Price (VWAP) benchmark, from the point of view of a risk-averse broker. The problem consists in minimizing mean-variance of the slippage, with…
In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…
Small operators who take part in secondary wireless spectrum markets typically have strict budget limits. In this paper, we study the bidding problem of a budget constrained operator in repeated secondary spectrum auctions. In existing…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of…
We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal…
This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…
In this paper, we develop a new method for finding an optimal biddingstrategy in sequential auctions, using a dynamic programming technique. Theexisting method assumes that the utility of a user is represented in anadditive form. Thus, the…