Related papers: On the valuation of arithmetic-average Asian optio…
For the OEIS sequence A025166, defined by $a(n) = -n!\,2^{n}\,L_{n}(1/2)$ where $L_{n}$ is the Laguerre polynomial of degree $n$, R.~J.~Mathar contributed in February 2013 the conjectured order-2 P-recursive recurrence \[ a(n) + (-4n+3)\,…
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic…
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…
In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using…
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.
The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a…
We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions.…
An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form $\sum_{i=1}^{\ell}q_i(t)\, D _t ^{\alpha_i} u(x,t)$, where the $q_i$ are continuous functions, each $D _t…
In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we…
We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian…
Artificial intelligence is transforming financial investment decision-making frameworks, with deep reinforcement learning demonstrating substantial potential in robo-advisory applications. This paper addresses the limitations of traditional…
Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
In Neri and Schneider (2012) we presented a method to recover the Maximum Entropy Density (MED) inferred from prices of call and digital options on a set of n strikes. To find the MED we need to numerically invert a one-dimensional function…
No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists,…
Generating functions $h_r(\tau)$ of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a…
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…
In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…
We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre and Jacobi ensembles for all the symmetry classes beta = 1,2, 4 and finite matrix dimension n. The moments of the Jacobi ensembles…