We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs. We consider a market with a single risky asset whose ask pr
In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on reservation prices (in place of the utility function). In this pap
Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from adverse selection risk by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liq
In this paper, we mainly study the impact of the implied certainty equivalent rate on investment in financial markets. First, we derived the mathematical expression of the implied certainty equivalent rate by using put-call parity, and then we selected some company stocks and options; we considered
The Consumer Financial Protection Bureau defines the notion of payoff amount as the amount that has to be payed at a particular time in order to completely pay off the debt, in case the lender intends to pay off the loan early, way before the last installment is due (CFPB 2020). This amount is well-
The stock segment of China’s time-honored brand enterprises has an important position in our securities stock market. The holiday effect is one of the market anomalies that occur in the securities market, which refers to the phenomenon that the stock market has significantly different returns than o
We study robust mean-variance optimization in multiperiod portfolio selection by allowing the true probability measure to be inside a Wasserstein ball centered at the empirical probability measure. Given the confidence level, the radius of the Wasserstein ball is determined by the empirical data. Th
This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided
Discount is the difference between the face value of a bond and its present value. I propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath–Jarrow–Morton framework for forward rates. I derive general consistency conditions for factor models, and
This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, u
Triangle fees are a novel fee structure for AMMs, in which marginal fees are decreasing in a trade’s size. That decline is proportional to the movement in the AMM’s implied price, i.e. for every basis point the trade moves the ratio of assets, the marginal fee declines by a basis point. These fees c
Central clearing counterparty houses (CCPs) play a fundamental role in mitigating the counterparty risk for exchange traded options. CCPs cover for possible losses during the liquidation of a defaulting member’s portfolio by collecting initial margins from their members. In this article we analyze t
The multifractal spectra of daily foreign exchange rates for US dollar (USD), the British Pound (GBP), the Euro (Euro) and the Japanese Yen (Yen) with respect to the Indian Rupee are analysed for the period 6th January 1999 to 24th July 2018. We observe that the time series of logarithmic returns of
This paper studies the q-learning, recently coined as the continuous time counterpart of Q-learning by Jia and Zhou (2023), for continuous time Mckean-Vlasov control problems in the setting of entropy-regularized reinforcement learning. In contrast to the single agent’s control problem in Jia and Zh
This paper introduces a novel framework for assessing risk and decision-making in the presence of uncertainty, the \emph{$\varphi$-Divergence Quadrangle}. This approach expands upon the traditional Risk Quadrangle, a model that quantifies uncertainty through four key components: \emph{risk, deviatio
This work seeks to answer key research questions regarding the viability of reinforcement learning over the S&P 500 index. The on-policy techniques of Value Iteration (VI) and State-action-reward-state-action (SARSA) are implemented along with the off-policy technique of Q-Learning. The models are t
The paper explores the concept of the \emph{expectile risk measure} within the framework of the Fundamental Risk Quadrangle (FRQ) theory. According to the FRQ theory, a quadrangle comprises four stochastic functions associated with a random variable: error'', regret’’, risk'', and deviation'
This study delves into the temporal dynamics within the equity market through the lens of bond traders. Recognizing that the riskless interest rate fluctuates over time, we leverage the Black-Derman-Toy model to trace its temporal evolution. To gain insights from a bond trader’s perspective, we focu
In this paper, we present a measure of time irreversibility using trend pattern statistics. We define the irreversibility index as the Kullback-Leibler divergence between the distribution of uptrends subsequences (increasing trends) and the corresponding downtrends subsequences distribution (decreas
Retirement prediction helps individuals and institutions make informed financial, lifestyle, and workforce decisions based on estimated retirement portfolios. This paper attempts to predict retirement using Monte Carlo simulations, allowing one to probabilistically account for a range of possibiliti