arXiv research

Efficiently calculates Brazilian stock options with discrete dividends.

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…

We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transform of general Gaussian processes in terms of Fredholm's determinant and…

Fast approximate inference for non-Gaussian data.

Let $x : M \to E^m$ be an isometric immersion of a Riemannian manifold $M$ into a Euclidean $m$-space. Denote by $Δ$ the Laplace operator of $M$. Then $Δ$ gives rise to a differentiable map $L :M \to E^m$, called the Laplace map, defined by $L(p)=(Δx)(p)$, $p\in M$. We call $L(M)$ the Laplace image, and the transformat…

The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Lap…

Study of line congruences for Appell's rank-4 hypergeometric functions.

The paper examines special Q-nets that terminate after a finite number of Laplace steps.

The paper studies graph Laplace operator behavior near isolated singularities.

In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating vari…

The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.

We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.

The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. T…

Study investigates ruin probability with random premiums and risky investments.

We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of $\R^d$ that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.

The study bounds quantum eigenfunctions on complex manifolds.

In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal th…

Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.

Asymptotic Laplace transform for geometric Brownian motion applied to bond pricing.

This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…

Extend classical theory of affine processes to path-dependent setting

The study bounds Riesz transforms on manifolds with controlled curvature.

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…

Develops a new method to compute risk-sharing allocations using Laplace transforms.

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values o…

Study efficient pricing for barrier options in stochastic-volatility models with leverage correction.

New techniques save bits in image compression with upsampling.

This paper adresses the valuation of the Paris barrier options proposed by Yor, Jeanblanc-Picque, and Chesnay (Advances in Applied Probability, 29(1997), 165-184) using the Laplace transform approach. Based on suggestions by Pliska the notion of Paris options is extended such that their valuation is possible at any poi…

We study the problem of utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset. The asset price dynamics follow a diffusion process with regime-switching coefficients modeled by a continuous-time finite-state Markov chain. We consider an inves…

We propose an affine extension of the Linear Gaussian term structure Model (LGM) such that the instantaneous covariation of the factors is given by an affine process on semidefinite positive matrices. First, we set up the model and present some important properties concerning the Laplace transform of the factors and th…

New method calculates geometric Brownian motion with affine drift and its integral.

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of correspondin…

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…

The paper uses the variance-gamma model to price options and explain excess kurtosis.

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …

In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…

In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an explicit matrix Wiener-Ho…

It is proved that if a Paley-Wiener family of eigenfunctions of the Laplace operator in $\mathbb R^3$ vanishes on a real analytically ruled two-dimensional surface $S \subset \mathbb R^3$ then $S$ is a union of cones, each of which is contained in a translate of the zero set of a nonzero harmonic homogeneous polynomial…

This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…

Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.

Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly computing the transform and its inverse in order to apply other network operati…

A new method combines ANN and Laplace for fast Bayesian inference in ODE models.

Efficiently transforms samples from various statistical models.

New methods for computing volumes and constructing Fano fibrations.

The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.

We consider vector fields $X$ on a closed manifold $M$ with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class $ξ\in H^1(M;\mathbb R)$ which is Lyapunov for $X$ defines counting functions for isolated instantons and closed trajectories. If $X$ has exponent…

In this paper we propose a transform method to compute the prices and greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with hyper-exponential jumps. In…

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…