数理金融
With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR)…
In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees…
We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…
This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for $N$-period market models and demonstrate that, when the…
In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality…
We study the expected utility maximization problem of a large investor who is allowed to make transactions on tradable assets in an incomplete financial market with endogenous permanent market impacts. The asset prices are assumed to follow…
We develop a mathematical framework to optimize leveraged staking ("loopy") strategies in Decentralized Finance (DeFi), in which a staked asset is supplied as collateral, the underlying is borrowed and re-staked, and the loop can be…
This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the…
No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset…
An agent holds a position in a perpetual contract with payoff function $\psi$ and attempts to liquidate the position while managing transaction costs, inventory risk, and funding rate payments. By solving the agent's stochastic control…
We investigate a class of non-Markovian processes that hold particular relevance in the realm of mathematical finance. This family encompasses path-dependent volatility models, including those pioneered by [Platen and Rendek, 2018] and,…
Classical Kyle-type models of informed trading typically treat noise trader demand as purely exogenous. In reality, many market participants react to price movements and news, generating feedback effects that can significantly alter market…
Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic…
We study portfolio choice when firm-level emissions intensities are measured with error. We introduce a scope-specific penalty operator that rescales asset payoffs as a smooth function of revenue-normalized emissions intensity. Under payoff…
This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a…
We study approximation limits of single-hidden-layer neural networks with analytic activation functions under global coefficient constraints. Under uniform $\ell^1$ bounds, or more generally sub-exponential growth of the coefficients, we…
We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a…
We study contagion and systemic risk in sparse financial networks with balance-sheet interactions on a directed random graph. Each institution has homogeneous liabilities and equity, and exposures along outgoing edges are split equally…
We study the optimal liquidation of a large position on Uniswap v2 and Uniswap v3 in discrete time. The instantaneous price impact is derived from the AMM pricing rule. Transient impact is modeled to capture either exponential or…
The Lambda Value-at-Risk (Lambda-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk…