arXiv subjects

Siddhartha P. Chakrabarty

Publications and source records attributed to Siddhartha P. Chakrabarty.

At least 19 recordsLinked to original sources

arXiv2025

Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach

We present a novel approach for the bank's decision problem, incorporating Limited Liability in the objective function. Accordingly, we consider continuous time models, with and without Limited Liability. We compare the solutions of these two models to demonstrate the effect of inclusion of Limited Liability. To solve the problem with the objective function incorporating Limited Liability, we approximate the payoff function to another set of functions for which we have closed-form solutions. Then, we show that the solution with Limited Liability incorporates less risky assets, while simultaneously increasing the resilience of the bank. After that, we use the metric of $Distance~to~Default$, from the KMV Model, to analyze the bank's resiliency, by considering that the interest rate follows the Vasicek model. Finally, we illustrate the results obtained with a numerical example.

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arXiv2025

Strategic Control of Drug-Resistant HIV: Multi-Strain Modeling with Diagnosis, Adherence, and Treatment Switching

A central challenge in Human Immunodeficiency Virus (HIV) public health policy lies in determining whether to universally expand treatment access, despite the risk of sub-optimal adherence and consequent drug resistance, or to adopt a more strategic allocation of resources that balances treatment coverage with adherence support. This dilemma is further complicated by the need for timely switching to second-line therapy, which is critical for managing treatment failure but imposes additional burdens on limited healthcare resources. In this study, we develop and analyze a compartmental model of HIV transmission that incorporates both drug-sensitive and drug-resistant strains, diagnosis status, and treatment progression, including switching to second-line therapy upon detection of resistance. Basic reproduction numbers for both strains are derived, and equilibrium analysis reveals the existence of a disease-free state and two endemic states, where the drug-sensitive strain may be eliminated while the drug-resistant strain persists. Local and global sensitivity analyses are performed, using partial rank correlation coefficient (PRCC) and Sobol methods, to identify key parameters influencing different model outcomes. We extend the model using optimal control theory to assess multiple intervention strategies targeting diagnosis, treatment initiation, and adherence. A novel dynamic control framework is proposed to achieve the UNAIDS 95-95-95 targets through efficient resource allocation. Numerical simulations validate the analytical results and compare the effectiveness and cost-efficiency of control strategies. Our findings highlight that long-term HIV epidemic control depends critically on prioritizing adherence-focused interventions alongside efforts to expand first-line treatment coverage.

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arXiv2025

Machine Learning Based Stress Testing Framework for Indian Financial Market Portfolios

This paper presents a machine learning driven framework for sectoral stress testing in the Indian financial market, focusing on financial services, information technology, energy, consumer goods, and pharmaceuticals. Initially, we address the limitations observed in conventional stress testing through dimensionality reduction and latent factor modeling via Principal Component Analysis and Autoencoders. Building on this, we extend the methodology using Variational Autoencoders, which introduces a probabilistic structure to the latent space. This enables Monte Carlo-based scenario generation, allowing for more nuanced, distribution-aware simulation of stressed market conditions. The proposed framework captures complex non-linear dependencies and supports risk estimation through Value-at-Risk and Expected Shortfall. Together, these pipelines demonstrate the potential of Machine Learning approaches to improve the flexibility, robustness, and realism of financial stress testing.

q-fin.RM↗

arXiv2025

Dynamic loan portfolio management in a three time step model

This paper studies the bank dynamic decision problem in the intermediate time step for a discrete-time setup. We have considered a three-time-step model. Initially, the banks raise money through debt and equity and invest in different types of loans. It liquidates its assets and raises new funds at the intermediate-time step to meet the short-term debt holders claim. Further, it has to meet specific capital requirements given by the regulators. In this work, we have theoretically studied the effect of raising new equity and debt. We show that in some cases, raising equity and debt may increase the return on equity, and in some cases, it may decrease the return on equity. We have discussed several cases and given a bound on the capital that can be raised. We have added an equity holders constraint, which ensures the return on equity and desists the bank from defaulting at the final time point.

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arXiv2024

Multilevel Monte Carlo in Sample Average Approximation: Convergence, Complexity and Application

In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the computational efficiency of solving optimization problems. In this context, we conduct a thorough analysis, exploiting Cramér's large deviation theory, to establish uniform convergence, quantify the convergence rate, and determine the sample complexity for both standard Monte Carlo and MLMC paradigms. Additionally, we perform a root-mean-squared error analysis utilizing tools from empirical process theory to derive sample complexity without relying on the finite moment condition typically required for uniform convergence results. Finally, we validate our findings and demonstrate the advantages of the MLMC estimator through numerical examples, estimating Conditional Value-at-Risk (CVaR) in the Geometric Brownian Motion and nested expectation framework.

q-fin.CP↗

arXiv2024

The Carbon Premium: Correlation or Causation? Evidence from S&P 500 Companies

In the context of whether investors are aware of carbon-related risks, it is often hypothesized that there may be a carbon premium in the value of stocks of firms, conferring an abnormal excess value to firms' shares as a form of compensation to investors for their transition risk exposure through the ownership of carbon instensive stocks. However, there is little consensus in the literature regarding the existence of such a premium. Moreover few studies have examined whether the correlation that is often observed is actually causal. The pertinent question is whether more polluting firms give higher returns or do firms with high returns have less incentive to decarbonize? In this study, we investigate whether firms' emissions is causally linked to the presence of a carbon premium in a panel of 141 firms listed in the S\&P500 index using fixed-effects analysis, with propensity score weighting to control for selection bias in which firms increase their emissions. We find that there is a statistically significant positive carbon premium associated with Scope 1 emissions, while there is no significant premium associated with Scope 2 emissions, implying that risks associated with direct emissions by the firm are priced, while bought emissions are not.

q-fin.PR↗

arXiv2024

ESG driven pairs algorithm for sustainable trading: Analysis from the Indian market

This paper proposes an algorithmic trading framework integrating Environmental, Social, and Governance (ESG) ratings with a pairs trading strategy. It addresses the demand for socially responsible investment solutions by developing a unique algorithm blending ESG data with methods for identifying co-integrated stocks. This allows selecting profitable pairs adhering to ESG principles. Further, it incorporates technical indicators for optimal trade execution within this sustainability framework. Extensive back-testing provides evidence of the model's effectiveness, consistently generating positive returns exceeding conventional pairs trading strategies, while upholding ESG principles. This paves the way for a transformative approach to algorithmic trading, offering insights for investors, policymakers, and academics.

q-fin.TR↗

arXiv2023

Loan portfolio management and Liquidity Risk: The impact of limited liability and haircut

In this article, we consider the problem of a bank's loan portfolio in the context of liquidity risk, while allowing for the limited liability protection enjoyed by the bank. Accordingly, we construct a novel loan portfolio model with limited liability, while maintaining a threshold level of haircut in the portfolio. For the constructed three-time step loan portfolio, at the initial time, the bank raises capital via debt and equity, investing the same in several classes of loans, while at the final time, the bank either meets its liabilities or becomes insolvent. At the intermediate time step, a fraction of the deposits are withdrawn, resulting in liquidation of some of the bank's assets. The liquidated portfolio is designed with the goal of minimizing the liquidation cost. Our theoretical results show that model with the haircut constraint leads to lesser liquidity risk, as compared to the scenario of no haircut constraint being imposed. Finally, we present numerical results to illustrate the theoretical results which were obtained.

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arXiv2023

Green portfolio optimization: A scenario analysis and stress testing based novel approach for sustainable investing in the paradigm Indian markets

In this article, we present a novel approach for the construction of an environment-friendly green portfolio using the ESG ratings, and application of the modern portfolio theory to present what we call as the ``green efficient frontier'' (wherein the environmental score is included as a third dimension to the traditional mean-variance framework). Based on the prevailing action levels and policies, as well as additional market information, scenario analyses and stress testing are conducted to anticipate the future performance of the green portfolio in varying circumstances. The performance of the green portfolio is evaluated against the market returns in order to highlight the importance of sustainable investing and recognizing climate risk as a significant risk factor in financial analysis.

q-fin.PM↗

arXiv2022

Classification based credit risk analysis: The case of Lending Club

In this paper, we performs a credit risk analysis, on the data of past loan applicants of a company named Lending Club. The calculation required the use of exploratory data analysis and machine learning classification algorithms, namely, Logistic Regression and Random Forest Algorithm. We further used the calculated probability of default to design a credit derivative based on the idea of a Credit Default Swap, to hedge against an event of default. The results on the test set are presented using various performance measures.

q-fin.RM↗

arXiv2022

Multilevel Monte Carlo and its Applications in Financial Engineering

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two subareas, namely, option pricing and financial risk management. For the former, the discussion involves incorporation of the importance sampling algorithm, in conjunction with the MLMC estimator, thereby constructing a hybrid algorithm in order to achieve reduction for the overall variance of the estimator. In case of the latter, we discuss the studies carried out in order to construct an efficient algorithm in order to estimate the risk measures of Value-at-Risk (VaR) and Conditional Var (CVaR), in an efficient manner. In this regard, we briefly discuss the motivation and the construction of an adaptive sampling algorithm with an aim to efficiently estimate the nested expectation, which, in general is computationally expensive.

q-fin.CP↗

arXiv2022

Does limited liability reduce leveraged risk?: The case of loan portfolio management

Return-risk models are the two pillars of modern portfolio theory, which are widely used to make decisions in choosing the loan portfolio of a bank. Banks and other financial institutions are subjected to limited liability protection. However, in most of the model formulation, limited liability is not taken into consideration. Accordingly, to address this, we have, in this article, analyzed the effect of including it in the model formulation. We formulate four models, two of them are maximizing the expected return with risk constraint, including and excluding limited-liability, and other two are minimization of risk with threshold level of return with and without limited-liability. Our theoretical results show that the solutions of the models with limited-liability produce better results than the others, in both minimizing risk and maximizing expected return. It has less risky investment than the other portfolio that solves the other model. Finally, an illustrative example is presented to support the theoretical results obtained.

q-fin.PM↗

arXiv2022

Multilevel Richardson-Romberg and Importance Sampling in Derivative Pricing

In this paper, we propose and analyze a novel combination of multilevel Richardson-Romberg (ML2R) and importance sampling algorithm, with the aim of reducing the overall computational time, while achieving desired root-mean-squared error while pricing. We develop an idea to construct the Monte-Carlo estimator that deals with the parametric change of measure. We rely on the Robbins-Monro algorithm with projection, in order to approximate optimal change of measure parameter, for various levels of resolution in our multilevel algorithm. Furthermore, we propose incorporating discretization schemes with higher-order strong convergence, in order to simulate the underlying stochastic differential equations (SDEs) thereby achieving better accuracy. In order to do so, we study the Central Limit Theorem for the general multilevel algorithm. Further, we study the asymptotic behavior of our estimator, thereby proving the Strong Law of Large Numbers. Finally, we present numerical results to substantiate the efficacy of our developed algorithm.

q-fin.CP↗

arXiv2022

Studying the age of onset and detection of Chronic Myeloid Leukemia using a three-stage stochastic model

Chronic Myeloid Leukemia (CML) is a biphasic malignant clonal disorder that progresses, first with a chronic phase, where the cells have enhanced proliferation only, and then to a blast phase, where the cells have the ability of self-renewal. It is well-recognized that the Philadelphia chromosome (which contains the BCR-ABL fusion gene) is the "hallmark of CML". However, empirical studies have shown that the mere presence of BCR-ABL may not be a sufficient condition for the development of CML, and further modifications related to tumor suppressors may be necessary. Accordingly, we develop a three-mutation stochastic model of CML progression, with the three stages corresponding to the non-malignant cells with BCR-ABL presence, the malignant cells in the chronic phase and the malignant cells in the blast phase. We demonstrate that the model predictions agree with age incidence data from the United States. Finally, we develop a framework for the retrospective estimation of the time of onset of malignancy, from the time of detection of the cancer.

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arXiv2022

Leverage Ratio: An empirical study of the European banking system

This paper empirically analyzes a dataset published by the European Banking Authority. Our main aim was to study how the Leverage Ratio is affected by adverse financial scenarios. This was be followed by observing how Leverage Ratio exposures are correlated to various other financial variables and how various regression techniques can be used to explain the correlation.

q-fin.RM↗

arXiv2022

Single Event Transition Risk: A Measure for Long Term Carbon Exposure

Although there is a growing consensus that a low-carbon transition will be necessary to mitigate the accelerated climate change, the magnitude of transition-risk for investors is difficult to measure exactly. Investors are therefore constrained by the unavailability of suitable measures to quantify the magnitude of the risk and are forced to use the likes of absolute emissions data or ESG scores in order to manage their portfolios. In this article, we define the Single Event Transition Risk (SETR) and illustrate how it can be used to approximate the magnitude of the total exposure of the price of a share to low-carbon transition. We also discuss potential applications of the single event framework and the SETR as a risk measure and discuss future direction on how this can be extended to a system with multiple transition events.

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arXiv2022

Progression, Detection and Remission: Evolution of Chronic Myeloid Leukemia using a three-stage probabilistic model

We present a three-stage probabilistic model for the progression of Chronic Myeloid Leukemia (CML), as manifested by the leukemic stem cells, progenitor cells and mature leukemic cells. This progression is captured through the process of cell division and cell mutation, with probabilities of occurrence being assigned to both of them. The key contributions of this study include, the determination of the expected number of the leukemic stem cells, progenitor cells, mature leukemic cells, as well as total number of these cells (in terms of probabilities, and contingent on the initial cell count), expected time to reach a threshold level of total and injurious leukemic cells, as well as the critical time when the disease changes its phases, the probability of extinction of CML, and the dynamics of CML evolution consequent to primary therapy. Finally, the results obtained are demonstrated with numerical illustrations.

q-bio.PE↗

arXiv2022

Modeling the dynamics of COVID-19 transmission in India: Social Distancing, Regional Spread and Healthcare Capacity

In the new paradigm of health-centric governance, policy makers are in a constant need for appropriate metrics and estimates in order to determine the best policies in a non-arbitrary fashion. Thus, in this paper, a compartmentalized model for the transmission of COVID-19 is developed to facilitate policy making. A socially distanced compartment is added to the model and its utility in quantifying the magnitude of voluntary social distancing is illustrated. Modifications are made to incorporate inter-region migration, and suitable metrics are proposed to quantify the impact of migration on the rise of cases. The healthcare capacity is modeled and a method is developed to study the consequences of the saturation of the healthcare system. The model and related measures are used to study the nature of the transmission and spread of COVID-19 in India, and appropriate insights are drawn.

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