Related papers: Multilinear Superhedging of Lookback Options
We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this…
In this work we offer an $O(|V|^2 |E|\, W)$ pseudo-polynomial time deterministic algorithm for solving the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games. This improves by a factor $\log(|V|\, W)$ the best previously…
This paper investigates portfolio selection within a continuous-time financial market with regime-switching and beliefs-dependent utilities. The market coefficients and the investor's utility function both depend on the market regime, which…
We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen…
We study pricing and (super)hedging for American options in an imperfect market model with default, where the imperfections are taken into account via the nonlinearity of the wealth dynamics. The payoff is given by an RCLL adapted process…
Min-max optimization problems (i.e., min-max games) have been attracting a great deal of attention because of their applicability to a wide range of machine learning problems. Although significant progress has been made recently, the…
Gameplay under various forms of uncertainty has been widely studied. Feldman et al. (2010) studied a particularly low-information setting in which one observes the opponent's actions but no payoffs, not even one's own, and introduced an…
In 1956 John Kelly wrote a paper at Bell Labs describing the relationship between gambling and Information Theory. What came to be known as the Kelly Criterion is both an objective and a closed-form solution to sizing wagers when odds and…
When selling many goods with independent valuations, we develop a distributionally robust framework, consisting of a two-player game between seller and nature. The seller has only limited knowledge about the value distribution. The seller…
This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm…
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space…
In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth. Going beyond existing literature, our focal point here is the rebalancing frequency…
We investigate the strategic surplus obtainable against a Follow-the-Regularized-Leader (FTRL) learner with constant step size $\eta$ in $n\times m$ two-player zero-sum games played over $T$ rounds against a clairvoyant optimizer. In…
This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
We consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate…
A competing market model with a polyvariant profit function that assumes "zeitnot" stock behavior of clients is formulated within the banking portfolio medium and then analyzed from the perspective of devising optimal strategies. An…
We prove new upper and lower bounds for sample complexity of finding an $\epsilon$-optimal policy of an infinite-horizon average-reward Markov decision process (MDP) given access to a generative model. When the mixing time of the…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization…