arXiv research

The paper develops a UCB-based method for a specific class of restless bandit problems.

We determine Kelly criterion for a game with variable pay-off. The Kelly fraction satisfies a fundamental integral equation and is smaller than the classical Kelly fraction for the same game with the constant average pay-off.

Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-…

We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, $N$ agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off 1, others zero. The agents optimize the expectation value of their discounted fu…

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice …

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We…

A new algorithm for restless bandits handles long-range dependencies.

Study Nash equilibrium in non-zero-sum game with Bermudan strategies.

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…

Swing options on the gas market are american style option where daily quantities exercices are constrained and global quantities exerciced each year constrained too. The option holder has to decide each day how much he consumes of the quantities satisfying the constraints and tries to use a strategy in order to maximiz…

In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realised volatilit…

Model evaluates insurance risk using thermodynamic principles.

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processe…

This research uses empirical copulas to price quanto options, showing significant differences from traditional models.

Paper shows how LSTM can remember long sequences by attending to persisted information.

We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…

We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential…

Optimal stopping problem solved for irregular reward processes without regularity assumptions.

This paper studies the payoff amounts in simple interest loans without arbitrage.

Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide downside protection. A tractable stochastic mortality model with age dependent …

New model values equity-linked securities with guaranteed return.

In this paper we characterise the propensity of big capital investments to systematically deliver poor outcomes as "fragility," a notion suggested by Nassim Taleb. A thing or system that is easily harmed by randomness is fragile. We argue that, contrary to their appearance, big capital investments break easily - i.e. d…

This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times for a firm. Recorded default occurs when default is recorded in the legal system. The economic default time is the last time when the firm is able to pay off its debt prior to the legal defa…

We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\…

New models explain rough and persistent volatility patterns.

New definition resolves ambiguity in non-stationary bandit classification.

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge ex…

New algorithms cluster non-stationary time series data.

The method approximates stationary distributions of Markov models by truncating irrelevant states.

Proposes a new algorithm for non-stationary bandits.

New kernels model non-stationary data efficiently.

The paper classifies ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia.

SmoothFBO tackles non-stationary functional bilevel optimization.

A Hamiltonian stationary Lagrangian submanifold of a Kaehler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kaehler manifold of real dimension four that guarantees the existence of a family of small Hamiltonian stationar…

Proposes a method to forecast non-stationary time series.

Method proves ellipticity of vacuum spacetime boundary problems.

Flexible non-stationary modeling of spatial outcomes using a mixed-stationary Gaussian process.

The paper simplifies arguments for stationary varifolds results.

This is the second part of the investigation started in [Stationary solutions and asymptotic flatness I]. We prove here that Strongly Stationary ends having cubic volume growth are Weakly Asymptotically Flat. Combined with the results of the previous paper this shows that Strongly Stationary ends are Asymptotically Fla…

Study finds sample size needed for non-stationary model selection.

The paper improves energy decay estimates for Dir-stationary Q-valued functions and applies them to Liouville-type theorems and continuity.

The study proves compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces.

Study on fake stationary Volterra Heston model for non-stationary processes.

We study surfaces in TN that are area-stationary with respect to a neutral Kaehler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are area-stationary are also holomorphic and hence totally null. However, in general, are…

Two classification results for stationary surfaces of least moment of inertia.

Algorithm minimizes regret in non-stationary dueling bandits with unknown parameters.