A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper provides closed-form time derivatives for rigid body systems.
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique…
Develops semi-closed form solutions for barrier and American options on time-dependent OU process.
For a fundamental solution of Laplace's equation on the -radius -dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion for a fundamental solution of Laplace's equation in hyperspherical geometry in geo…
We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We …
We consider the Cauchy problem associated with a general parabolic partial differential equation in dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provi…
Paper derives closed-form solutions for CEV model using semiclassical approximation.
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation in which the volatility function may depend on the second derivative of the opti…
The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a closed form solution of the HJB equation for power utility due to its homothetic pr…
Paper improves basket option pricing for log-normal models.
Derives semi-closed form prices for barrier options in the Hull-White model.
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…
Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trad…
New model captures complex relationships from experimental data.
Stable blowup solutions found for supercritical Yang-Mills equations.
We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of game-theoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem is reduced to a backward induction of an optimization over simplexes. For Europe…
EML-CD discovers causal mechanisms from neural networks in a structured way.
New method for linear connections in ODEs with constraints.
This note justifies approximations of arithmetic forwards using weighted averages of overnight forwards.
This paper extends barrier option pricing to CIR and CEV models using semi-closed form solutions.
We solve the mean parametrization of von Mises-Fisher distribution.
We study the effect of parameters uncertainties on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, thanks to Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to hedging procedures in order to compute the sensitivities of SDE trajectories with respect…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra of symmetries has invariant solutions with respect to this Lie alge…
Proposes IPT for modeling complex joint distributions.
We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter …
We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic P…
The abstract discusses vector fields on curved spaces and conservation laws.
Closed-form solutions derived for perpetual options under insider models.
Derives exact formula for Minkowski sum of ellipsoids in N-space.
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…
This paper summarizes closed-form relations for SE(3) maps and their derivatives.
Developed moment estimators for affine stochastic volatility models.
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present …
Motivated by the relationship between symplectic fibrations and classical Yang-Mills theories, we study the closeness of a -form (n=2,3) defined on the total space of a fibration as a simple model for an abstract field theory. We introduce 2-plectic fibrations and interpret geometrically the corresponding equations …
Our main aim is to present a geometrically meaningful formula for the fundamental solutions to a second order sub-elliptic differential equation and to the heat equation associated with a sub-elliptic operator in the sub-Riemannian geometry on the unit sphere . Our method is based on the Hamiltonian approa…
We have created a framework for analyzing subscription based businesses in terms of a unified metric which we call SCV (single customer value). The major advance in this paper is to model customer churn as an exponential decay variable, which directly follows from experimental data relating to subscription based busine…
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter . A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1…
ECSEL learns signomial equations for explainable classification.
We solve a Schrödinger bridge with a quadratic state cost, finding a closed-form solution.
We deal with the interest rate model proposed by Schaefer and Schwartz, which models the long rate and the spread, defined as the difference between the short and the long rates. The approximate analytical formula for the bond prices suggested by the authors requires a computation of a certain constant, defined via a n…
We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation. In this equation, not only its right hand side is known approximately, but also the integral operator is defined approximately. We show that this ill-posed problem has a rigorous …
Proves equations for high-dimensional gradient-based methods from Gaussian data.
On a generalized complex manifold there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. This notion in the case of an ordinary complex structure yields an object which we call a co-Higgs bundle and we consider the B-field action of a closed form of type (1,1), both local and gl…
Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalize…
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in advance. Both the investment criterion and the optimal strategy are characterized by th…
Modified perturbation method removes non-smoothness in solving Black-Scholes equations.
More and more AI services are provided through APIs on cloud where predictive models are hidden behind APIs. To build trust with users and reduce potential application risk, it is important to interpret how such predictive models hidden behind APIs make their decisions. The biggest challenge of interpreting such predic…