数理金融

This note explores the theoretical justification for some approximations of arithmetic forwards ($F_a$) with weighted averages of overnight (ON) forwards ($F_k$). The central equation presented in this analysis is: \begin{equation*}…

We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…

We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The…

We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…

This paper explores the application and significance of the second-order Esscher pricing model in option pricing and risk management. We split the study into two main parts. First, we focus on the constant jump diffusion (CJD) case,…

Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often…

We study the anticipating version of the classical portfolio optimization problem in a financial market with the presence of a trader who possesses privileged information about the future (insider information), but who is also subjected to…

We are considering the problem of optimal portfolio delegation between an investor and a portfolio manager under a random default time. We focus on a novel variation of the Principal-Agent problem adapted to this framework. We address the…

This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual…

We study the price impact of storage facilities in electricity markets and analyze the long-term profitability of these facilities in prospective scenarios of energy transition. To this end, we begin by characterizing the optimal operating…

Decentralized finance (DeFi) has revolutionized the financial landscape, with protocols like Uniswap offering innovative automated market-making mechanisms. This article explores the development of a backtesting framework specifically…

In a seminal paper, F. Delbaen and W. Schachermayer proved that the classical NA ("no arbitrage") condition implies the existence of an "absolutely continuous local martingale measure" (ACLMM). It is known that in general the existence of…

As an introduction to a Special Issue of International Journal of Theoretical and Applied Finance in Honour of the Memory of Thomas Robert Hurd we present a brief synopsis of Tom Hurd's scientific career and a bibliography of his scientific…

We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the…

We define a new model using a Hawkes process as a subordinator in a standard Brownian motion. We demonstrate that this Hawkes subordinated Brownian motion or more succinctly, variance-Hawkes process can be fit to 2018 and 2019 natural gas…

We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing…

We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…

Equity market dynamics are conventionally investigated in name space where stocks are indexed by company names. In contrast, by indexing stocks based on their ranks in capitalization, we gain a different perspective of market dynamics in…

We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets…

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find…