arXiv research

Paper tackles multiplayer symmetric games, securing equal share for n players.

In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to nonparametrically price and hed…

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities…

Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy …

The paper examines bounds for stop-loss payoffs using transformed random variables.

A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure…

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security prici…

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of st…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The …

In this article we show that the payment flow of a linear tax on trading gains from a security with a semimartingale price process can be constructed for all càglàd and adapted trading strategies. It is characterized as the unique continuous extension of the tax payments for elementary strategies w.r.t. the convergence…

The paper explores arbitrage opportunities in derivative markets under specific conditions.

This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which maximizes the growth ra…

Method constructs CFMMs matching desired payoffs.

Optimal payoff choice constrained by Bregman-Wasserstein divergence.

Optimal portfolio yields a digital option payoff.

Study finds cheapest possible payoff under ambiguity, linking to maxmin expected utility.

We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset. We show that these derivatives are dense in the space of continuous payoffs, a result that is exploited to quickly price arbitrary continuous payoffs. This approach …

The paper uncovers the impact of price and payoff autocorrelations in multi-period asset pricing models.

One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial position the set of those eligible payoffs that reduce the risk of the position to …

New method uses neural networks for better financial hedging.

Paper shows how to replicate payoffs without oracles in CFMMs.

We study a non-parametric multi-armed bandit problem with stochastic covariates, where a key complexity driver is the smoothness of payoff functions with respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases where it is a priori known how smooth the payoff functions are. I…

Game contingent claims (GCCs) generalize American contingent claims by allowing the writer to recall the option as long as it is not exercised, at the price of paying some penalty. In incomplete markets, an appealing approach is to analyze GCCs like their European and American counterparts by solving option holder's an…

American Depositary Receipts (ADRs) are exchange-traded certificates that rep- resent shares of non-U.S. company securities. They are major financial instruments for investing in foreign companies. Focusing on Asian ADRs in the context of asyn- chronous markets, we present methodologies and results of empirical analysi…

Develops a new method for robust risk measurement by averaging nearby payoffs.

Agent optimizes perpetual contract liquidation with transaction costs and risk.

Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new options that might give higher payoffs in the future. Although the study of band…

New findings show pure strategy equilibria are more robust in a war of attrition game.

This paper extends the Black-Scholes-Merton model to more complex market scenarios.

We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …

A time-dependent double-barrier option is a derivative security that delivers the terminal value $φ(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier opti…

New algorithms for stochastic linear bandits with heavy-tailed payoffs achieve nearly optimal regret.

This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff…

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our appr…

Study of $2 imes 2$ zero-sum games with noisy observations and commitments.

We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the payoff of these assets is not…

This paper studies robust payoff allocation in submodular games, especially against replication.

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and fo…

Study on optimal information acquisition in Kyle model with entropy cost.

We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such that the physical payoff distribution coincides with the (corrected) physical asset…

We derive a formula for liquidity providers' payoff on DEXs, linking it to volatility.

In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any c…

New decision-theoretic calibration error metric improves prediction reliability.

Quantum Monte Carlo speeds up option pricing for complex payoff functions.

New method uses DistRL to estimate entire payoff distribution for financial derivatives.

Optimizes a portfolio for an investor preferring accepted securities over a reference security.

We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action $i$, the learner receives information about the payoff of every action $j$ in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair $(i,j)$ (and may…