Related papers: Multilinear Superhedging of Lookback Options
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process.…
This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single…
In Stackelberg security games when information about the attacker's payoffs is uncertain, algorithms have been proposed to learn the optimal defender commitment by interacting with the attacker and observing their best responses. In this…
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The…
We consider an equity-linked contract whose payoff depends on the lifetime of policy holder and the stock price. We assume the limited capital for hedging and we provide with the best strategy for an insurance company in the meaning of so…
We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility…
A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…
We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set aside at least one coin showing heads;…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…
Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc. For these problems, gradient-based methods are well understood and enjoy strong guarantees. However, in the absence of convexity or…
For $n$ assets and discrete-time rebalancing, the probability to complete a given schedule of investments and withdrawals is maximized over progressively measurable portfolio weight functions. Applications consider two assets, namely the…
In this paper, I introduce a novel benchmark in games, super-Nash performance, and a solution concept, optimin, whereby players maximize their minimal payoff under unilateral profitable deviations by other players. Optimin achieves…
This work lies in the fusion of experimental economics and data mining. It continues author's previous work on mining behaviour rules of human subjects from experimental data, where game-theoretic predictions partially fail to work.…
We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she…