数理金融
The problem related to predicting dynamic volatility in financial market plays a crucial role in many contexts. We build a new generalized Barndorff-Nielsen and Shephard (BN-S) model suitable for uncertain environment with fuzziness and…
A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset to maximize the expected utility of the round-trip profit net of transaction costs. The optimization…
We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough…
This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy)…
We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible…
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how…
In this paper we introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results of [5], where a…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…
This paper investigates the impact of anonymous trading on the agents' strategy in an optimal execution framework. It mainly explores the specificity of order attribution on the Toronto Stock Exchange, where brokers can choose to either…
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and…
This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in…
In liquid option markets, W-shaped implied volatility curves have occasionally be observed. We show that such shapes can be reproduced in a mixture of two variance-gamma models. This is in contrast to lognormal models, where at least three…
US Institutions with more than $100 million assets under management must disclose part of their long positions into the SEC Form 13F-HR on a quarterly basis. We consider the number of variations in holdings between consecutive reporting…
In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential…
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the…
We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and…
The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of…
Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage…
We define data-driven macroeconomic regimes by clustering the relative performance in time of indices belonging to different asset classes. We then investigate lead-lag relationships within the regimes identified. Our study unravels market…