数理金融
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model…
We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set $\Xi\subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in…
This paper considers an optimal dividend distribution problem for an insurance company where the dividends are paid in a foreign currency. In the absence of dividend payments, our risk process follows a spectrally negative L\'evy process.…
Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities…
In this paper, we consider the problem of hedging Asian options in financial markets with transaction costs. For this, we use the asymptotic hedging approach. The main task of asymptotic hedging in financial markets with transaction costs…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
An open market is a subset of an entire equity market composed of a certain fixed number of top capitalization stocks. Though the number of stocks in the open market is fixed, the constituents of the market change over time as each…
We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in…
A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous…
Adachi and Ryu introduced a category Prob of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement in [Adachi and Ryu, 2019]. In this…
We prove a scaling limit theorem for the super-replication cost of options in a Cox--Ross--Rubinstein binomial model with transient price impact. The correct scaling turns out to keep the market depth parameter constant while resilience…
We derive an explicit solution for deterministic market impact parameters in the Graewe and Horst (2017) portfolio liquidation model. The model allows to combine various forms of market impact, namely instantaneous, permanent and temporary.…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To…
Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of \emph{insider information}. We assume that, since the…
We consider the issue of a market maker acting at the same time in the lit and dark pools of an exchange. The exchange wishes to establish a suitable make-take fees policy to attract transactions on its venues. We first solve the stochastic…