数理金融
We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options and we compute their non-trivial scaling limit for a vanishing price impact which is inversely…
Bernard et al. (2015) study an optimal insurance design problem where an individual's preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their…
This study introduces a new technique to recover the implicit discount factor in the derivative market using only European put and call prices: this discount is grounded in actual transactions in active markets. Moreover, this study…
We introduce a simple model for equity index derivatives. The model generalizes well known L\`evy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces…
In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional It\^o calculus approach, we overcome the non-Markovian and…
Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on…
Using techniques from deep learning (cf. [B\"uh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by [FL00]. Not only does…
In contrast to the usual procedure of estimating the distribution of a time series and then obtaining the quantile from the distribution, we develop a compensatory model to improve the quantile estimation under a given distribution…
In this article, we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein--Zin stochastic differential utility (EZ-SDU) who invests in a constant-parameter Black-Scholes-Merton market over the…
We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential…
In this paper, we examine the interlinkages among firms through a financial network where cross-holdings on both equity and debt are allowed. We relate mathematically the correlation among equities with the unconditional correlation of the…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
This paper develops a model for the bid and ask prices of a European type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend…
A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with…
In this paper, we present a computationally efficient technique based on the \emph{Method of Lines} (MOL) for the approximation of the Bermudan option values via the associated partial differential equations (PDEs). The MOL converts the…
This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
We detect the parameter sensitivities of bond pricing which is driven by a Brownian motion and a compound Poisson process as the discontinuous case in credit risk research. The strict mathematical deductions are given theoretically due to…
Securities borrowing and lending are critical to proper functioning of securities markets. To alleviate securities owners' exposure to borrower default risk, overcollateralization and indemnification are provided by the borrower and the…
We describe a way to complete a correlation matrix that is not fully specified. Such matrices often arise in financial applications when the number of stochastic variables becomes large or when several smaller models are combined in a…