arXiv research

Adversarial deep hedging learns to hedge without specifying asset price models.

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…

A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the underlying process. Thus, future knowledge of the …

Analyzes how long-term cash flows react to changes in underlying processes.

In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^{\infty}$ to the Dynkin's game…

We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The measures used include normalised generalised Gamma processes that demonstrate power …

We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this cla…

Geometrically proves majorizing measure theorem on Hadamard manifolds.

A new model aligns sequences using DPMM, outperforming GP-LVM.

The paper analyzes multivariate Hawkes processes and their induced population processes.

We solve the pricing problem for perpetual American puts and calls on dividend-paying assets. The dependence of a dividend process on the underlying stochastic factor is fairly general: any non-decreasing function is admissible. The stochastic factor follows a Levy process. This specification allows us to consider asse…

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary o…

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on…

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordina…

In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) Lévy processes to model the underlying asset of contingent claims. A DTC Lévy process is a generalized time-changed Lévy process whose continuous and pure jump parts are allowed to follow separate random time scal…

Unified approach for drawdown and drawup of Markov processes.

Modeling multiple Hawkes processes with shared dynamics using graphons.

Paper shows how sparse inversion speeds up log determinant derivatives.

Bayesian regularization improves policy performance in noisy MDPs.

Paper proves existence and uniqueness of solutions to PIDEs in Bessel spaces for option pricing.

Gaussian processes learn unknown ODE dynamics from sparse data.

We propose a mathematical procedure for finding informed trader activities in European-style options and their underlying asset. The regression model (9) with moving average component was written. Being added to it ARMA-process for log-price differences of underlying asset, the generalized model is written as Vector AR…

Neural models price financial options without assuming underlying price forms.

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long ho…

In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…

Active learning selects inputs for GPSSM to learn latent states.

This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential o…

The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.

Estimates stationary distribution from batch transitions without access to the underlying process.

Advanced kernels improve Gaussian process accuracy by incorporating domain knowledge.

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…

In this paper we present a very simple way to price a class of barrier options when the underlying process is driven by a huge class of Lévy processes. To achieve our goal we assume that our market satisfies a symmetry property. In case of not satisfying that property some approximations can be obtained.

Develops DSD for analyzing multiscale biological networks.

We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …

Study Markov cubature rules for polynomial processes.

The paper tackles learning to control systems with unknown parameters using Brownian noise.

For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to mo…

Develops Bilateral Gamma processes for financial market modeling.

This paper models insurance company insolvency using Lévy processes.

In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give some examples whose underlying assets behave as some popular Levy proc…

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed fi…

The intermarket analysis, in particular the lead-lag relationship, plays an important role within financial markets. Therefore a mathematical approach to be able to find interrelations between the price development of two different financial underlyings is developed in this paper. Computing the differences of the relat…

Study optimality in safety-constrained Markov decision processes using asynchronous value iteration and modified Q-learning.

Method learns latent SDEs from high-dimensional time series.

Paper tackles risk-sensitive impulse control for continuous-time processes.

For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is an exponential of an additive process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market a…

This paper extends Black-Scholes model for illiquid markets with jumps.