Constrained portfolio optimization in a life-cycle model ArXiv ID: 2410.20060 “View on arXiv” Authors: Unknown Abstract This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance. ...

Optimal life insurance and annuity decision under money illusion ArXiv ID: 2410.20128 “View on arXiv” Authors: Unknown Abstract This paper investigates the optimal consumption, investment, and life insurance/annuity decisions for a family in an inflationary economy under money illusion. The family can invest in a financial market that consists of nominal bonds, inflation-linked bonds, and a stock index. The breadwinner can also purchase life insurance or annuities that are available continuously. The family’s objective is to maximize the expected utility of a mixture of nominal and real consumption, as they partially overlook inflation and tend to think in terms of nominal rather than real monetary values. We formulate this life-cycle problem as a random horizon utility maximization problem and derive the optimal strategy. We calibrate our model to the U.S. data and demonstrate that money illusion increases life insurance demand for young adults and reduces annuity demand for retirees. Our findings indicate that the money illusion contributes to the annuity puzzle and highlights the role of financial literacy in an inflationary environment. ...

A Stock Price Prediction Approach Based on Time Series Decomposition and Multi-Scale CNN using OHLCT Images ArXiv ID: 2410.19291 “View on arXiv” Authors: Unknown Abstract Recently, deep learning in stock prediction has become an important branch. Image-based methods show potential by capturing complex visual patterns and spatial correlations, offering advantages in interpretability over time series models. However, image-based approaches are more prone to overfitting, hindering robust predictive performance. To improve accuracy, this paper proposes a novel method, named Sequence-based Multi-scale Fusion Regression Convolutional Neural Network (SMSFR-CNN), for predicting stock price movements in the China A-share market. By utilizing CNN to learn sequential features and combining them with image features, we improve the accuracy of stock trend prediction on the A-share market stock dataset. This approach reduces the search space for image features, stabilizes, and accelerates the training process. Extensive comparative experiments on 4,454 A-share stocks show that the model achieves a 61.15% positive predictive value and a 63.37% negative predictive value for the next 5 days, resulting in a total profit of 165.09%. ...

Double Auctions: Formalization and Automated Checkers ArXiv ID: 2410.18751 “View on arXiv” Authors: Unknown Abstract Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common objectives for determining the matching are maximizing trade volume at a uniform price and maximizing trade volume through dynamic pricing. Prior research has primarily focused on single-quantity trade requests. In this work, we extend the framework to handle multiple-quantity trade requests and present fully formalized matching algorithms for double auctions, along with their correctness proofs. We establish new uniqueness theorems, enabling automatic detection of violations in exchange systems by comparing their output to that of a verified program. All proofs are formalized in the Coq Proof Assistant, and we extract verified OCaml and Haskell programs that could serve as a resource for exchanges and market regulators. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm. ...

Dynamic Investment-Driven Insurance Pricing and Optimal Regulation ArXiv ID: 2410.18432 “View on arXiv” Authors: Unknown Abstract This paper analyzes the equilibrium of insurance market in a dynamic setting, focusing on the interaction between insurers’ underwriting and investment strategies. Three possible equilibrium outcomes are identified: a positive insurance market, a zero insurance market, and market failure. Our findings reveal why insurers may rationally accept underwriting losses by setting a negative safety loading while relying on investment profits, particularly when there is a negative correlation between insurance gains and financial returns. Additionally, we explore the impact of regulatory frictions, showing that while imposing a cost on investment can enhance social welfare under certain conditions, it may not always be necessary. ...

Generation of synthetic financial time series by diffusion models ArXiv ID: 2410.18897 “View on arXiv” Authors: Unknown Abstract Despite its practical significance, generating realistic synthetic financial time series is challenging due to statistical properties known as stylized facts, such as fat tails, volatility clustering, and seasonality patterns. Various generative models, including generative adversarial networks (GANs) and variational autoencoders (VAEs), have been employed to address this challenge, although no model yet satisfies all the stylized facts. We alternatively propose utilizing diffusion models, specifically denoising diffusion probabilistic models (DDPMs), to generate synthetic financial time series. This approach employs wavelet transformation to convert multiple time series (into images), such as stock prices, trading volumes, and spreads. Given these converted images, the model gains the ability to generate images that can be transformed back into realistic time series by inverse wavelet transformation. We demonstrate that our proposed approach satisfies stylized facts. ...

Loss Aversion and State-Dependent Linear Utility Functions for Monetary Returns ArXiv ID: 2410.19030 “View on arXiv” Authors: Unknown Abstract We present a theory of expected utility with state-dependent linear utility functions for monetary returns, that incorporates the possibility of loss-aversion. Our results relate to first order stochastic dominance, mean-preserving spread, increasing-concave linear utility profiles and risk aversion. As an application of the expected utility theory developed here, we analyze the contract that a monopolist would offer in an insurance market that allowed for partial coverage of loss. ...

What Drives Liquidity on Decentralized Exchanges? Evidence from the Uniswap Protocol ArXiv ID: 2410.19107 “View on arXiv” Authors: Unknown Abstract We study liquidity on decentralized exchanges (DEXs), identifying factors at the platform, blockchain, token pair, and liquidity pool levels with predictive power for market depth metrics. We introduce the v2 counterfactual spread metric, a novel criterion which assesses the degree of liquidity concentration in pools using the ``concentrated liquidity’’ mechanism, allowing us to decompose the effect of a factor on market depth into two channels: total value locked (TVL) and concentration. We further explore how external liquidity from competing DEXs and private inventory on DEX aggregators influence market depth. We find that (i) gas prices, returns, and a DEX’s share of trading volume affect liquidity through concentration, (ii) internalization of order flow by private market makers affects TVL but not the overall market depth, and (iii) volatility, fee revenue, and markout affect liquidity through both channels. ...

Enhancing literature review with LLM and NLP methods. Algorithmic trading case ArXiv ID: 2411.05013 “View on arXiv” Authors: Unknown Abstract This study utilizes machine learning algorithms to analyze and organize knowledge in the field of algorithmic trading. By filtering a dataset of 136 million research papers, we identified 14,342 relevant articles published between 1956 and Q1 2020. We compare traditional practices-such as keyword-based algorithms and embedding techniques-with state-of-the-art topic modeling methods that employ dimensionality reduction and clustering. This comparison allows us to assess the popularity and evolution of different approaches and themes within algorithmic trading. We demonstrate the usefulness of Natural Language Processing (NLP) in the automatic extraction of knowledge, highlighting the new possibilities created by the latest iterations of Large Language Models (LLMs) like ChatGPT. The rationale for focusing on this topic stems from our analysis, which reveals that research articles on algorithmic trading are increasing at a faster rate than the overall number of publications. While stocks and main indices comprise more than half of all assets considered, certain asset classes, such as cryptocurrencies, exhibit a much stronger growth trend. Machine learning models have become the most popular methods in recent years. The study demonstrates the efficacy of LLMs in refining datasets and addressing intricate questions about the analyzed articles, such as comparing the efficiency of different models. Our research shows that by decomposing tasks into smaller components and incorporating reasoning steps, we can effectively tackle complex questions supported by case analyses. This approach contributes to a deeper understanding of algorithmic trading methodologies and underscores the potential of advanced NLP techniques in literature reviews. ...

Periodic portfolio selection with quasi-hyperbolic discounting ArXiv ID: 2410.18240 “View on arXiv” Authors: Unknown Abstract We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we characterize the optimal portfolio for a pre-committing, naive and sophisticated agent respectively. In the more theoretically challenging problem with a sophisticated agent, the time-consistent planning strategy can be formulated as an equilibrium to a static mean field game. Interestingly, present bias and naivety do not necessarily result in less desirable risk taking behaviors, while agent’s sophistication may lead to excessive leverage (underinvestement) in the bad (good) states of the world. ...