数理金融

This paper considers finitely many investors who perform mean-variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average…

The geometric approach to financial markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by the two…

We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with…

We introduce a transport cohomological framework for categorical filtrations. Given a contravariant filtration $F:\mathcal T^{op}\to\mathbf{Prob}$ on a small category \(\mathcal T\), conditional expectation induces transport operators…

We identify the measurable absorbing obstruction to uniqueness of invariant probability measures for a Markov kernel. Ordinary absorbing decompositions obstruct global irreducibility and recurrence, but not necessarily uniqueness: an…

We explore a nuance to 'no arbitrage' in relation to 'information efficiency': acting immediately on an arbitrage is sometimes suboptimal; in such cases optimised trading can suppress the anticipation of predictable risk-outcomes, thereby…

This paper refutes the claim that the expected rate of return of the underlying asset plays no role in the Black-Scholes-Merton option pricing model.

We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for…

This paper studies optimal liquidity provision for perpetual contracts when the funding rate is a stochastic state variable. The core extension to classical market making is the coupling between inventory and funding payments: inventory…

We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial…

This research establishes ESG as a state dependent insurance mechanism against equity crashes by addressing the decoupling of unconditional alpha from tail risk resilience. By validating market stress regimes as distinct economic states…

Investor sentiment reflects the collective attitude of investors towards the asset, whether positive, negative or neutral. Market information, such as news and relevant social media posts, plays a significant role in shaping investor…

This paper introduces a new market-implied object, Time to Transition (TtT), extracted from the difference between two selected nodes of the greenium term structure. TtT is defined as the latent waiting time until this cross-maturity…

In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility…

We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the…

The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…

The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time…

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…

We introduce the Local Occupied Volatility (LOV) model that sits between Dupire's local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the…

For a sequence of binary bets, the Kelly criterion provides a closed-form solution that maximizes the expected growth rate of wealth. In contrast, when multiple bets are placed simultaneously (e.g., in portfolio allocation or prediction…