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King’s College has a large and thriving Financial Mathematics group, with an international reputation for research excellence.

Based in Central London in close proximity to the City of London, King’s has fostered strong links with industry practitioners and offers state of the art facilities, including a suite of high performance Bloomberg Terminals as used on real trading floors and other advanced computing facilities.

Mathematics has revolutionised the finance industry. Financial mathematics originated in the early 1970s with the seminal papers of Black, Scholes and Merton and has subsequently evolved into a trillion-dollar industry. The entire derivatives market relies upon financial mathematics, and the use of mathematical risk management principles is ubiquitous throughout the financial industry. In the wake of the financial crisis in 2008, the need for sound risk management and sophisticated, realistic modelling has been critical.

The mathematical techniques used in finance bring together a number of different branches of pure and applied mathematics, including but not limited to: probability, optimisation, functional analysis, partial differential equations, statistics, geometry, complex systems and numerical analysis. Moreover, financial mathematics has benefited from cross-fertilisation with other disciplines such as economics, operations research, theoretical physics, and computer science. Its relevance extends beyond finance into areas such as healthcare.

As a result, financial mathematics offers a wealth of research opportunities across pure and applied mathematics, and the research of the financial mathematics group at King’s reflects this diversity. We research questions as applied as how to invest your pension and as pure as the existence and uniqueness of solutions to infinite dimensional stochastic differential equations. Our faculty have diverse backgrounds in mathematics, physics, computing and the financial industry which results in a lively sharing of ideas.

We have forged excellent links with industry and regularly engage in collaborative research and consultancy projects with industry partners.

We are committed to active research of international excellence.

Members of the Financial Mathematics Group are available for in-house training in financial institutions on a wide range of specialised topics, and also regularly undertake consultancy projects in their areas of specialisation. Contact: teemu.pennanen@kcl.ac.uk.

People

John Armstrong

Reader in Financial Mathematics

Cristin Buescu

Senior Lecturer in Financial Mathematics

Feiyu Chen

PhD Student

James Dalby

Postdoctoral Research Associate in the Mathematical Modelling of Collective Pensions

Purba Das

Lecturer in Financial Mathematics

Publications

    Activities

    Cristin Buescu
    Recent research on portfolio optimization featured in interview of Dr Cristin Buescu by Faculti.Net

    A comparison of the effectiveness of Machine Learning vs Financial Mathematics techniques when optimally managing a portfolio of cointelated assets was presented in the recent research output of Dr Cristin Buescu, a member of the Financial Mathematics group at King’s.

    City of London
    The Practitioners’ Lecture Series Presents: Antoine Savine

    Workshop: Introduction to back-propagation and automatic adjoint differentiation (AAD) in machine learning and finance, 28-29 March 2019. This six-hour workshop included: Introduction to Artificial Neural Networks and Deep Learning; Back-propagation through ANNs; Applications of Deep Learning in Finance; Hands-on examples with Excel/C++ and Python/Tensor Flow; Extract computation graphs and differentiate arbitrary calculations; Fast (reverse mode) AAD with operator overloading in C++ Application to financial risk management. The Practitioners' Lecture Series at King's College London is organised by Dr Blanka Horvath and sponsored by Simudyne.

      Graphs
      FIPS 2018

      The eighth Workshop on Finance, Insurance, Probability and Statistics (FIPS 2018) brought together a global cast of leading academic experts, practitioners and junior researchers. Attendees shared research that underscored the contributions of probability and statistics to the development of quantitative models, methods, techniques and technologies in the fields of finance and insurance.

        Graph and equations
        Risk Management for Whales

        Thursday, 1 February 2018 Speaker: Lakshithe Wagalath (IESEG School of Management) Title: Risk Management for Whales Abstract: We propose a portfolio risk model which integrates market risk with liquidation costs. The model provides a framework for computing liquidation-adjusted risk measures such as Liquidation-adjusted VaR (LVaR). Calculation of liquidation-adjusted Value-at-Risk (LVaR) for simulated and real-life examples reveals a substantial impact of liquidation costs on portfolio risk for portfolios with large concentrated positions. This is joint work with Rama Cont.

          London skyline
          Optimisation in energy markets

          Optimization in energy markets, 3 April 2017 Speaker 1: Michel De Lara, École des Ponts ParisTech Title: Game Theory with Information: a Framework for the New Energy Systems Speaker 2: Pierre Carpentier, École des Ponts ParisTech Title: Optimization of Energy Production and Transport: Approaches by Decomposition Under Stochasticity Speaker 3: Jean-Philippe Chancelier, École des Ponts ParisTech Title: Stochastic Spatial Decomposition for Large Scale Hydro Valleys Speaker 4: Teemu Pennanen, King's College London Title: Mathematical models for pricing and hedging of delivery contracts

            City of London skyline
            Convex Analysis Seminar

            Convex Analysis Seminar, 30 March 2017 Speaker 1: Ari-Pekka Perkkiö, LMU Mathematics Institute Title: Regular processes and duality Abstract: We study the optional projection on spaces of cadlag and continuous processes. Our main results sharpen those of [Bismut, 1978] in cases where the projected process has additional integrability properties. Moreover, we characterize the topological duals of optional cadlag processes and of regular processes with the given integrability properties. Our main results are derived by purely functional analytic arguments simplifying original proofs of [Bismut, 1978]. We also present results on dual representations for convex integral functionals on regular processes. These yield a maximum principle for a general class of singular stochastic control problems. The talk is based on a joint work with TeemuPennanen. Speaker 2: Christian Léonard, Université Paris Ouest Title: Some results about entropic transport Abstract: Optimal transport is a powerful tool for proving several functional inequalities such as: concentration inequalities, geometric inequalities (Prekopa-Leindler inequality) or entropy-entropy production inequalities related to rates of convergence to equilibrium of heat flows. In this talk, an alternate similar approach will be introduced. It relies on entropic transport rather than standard optimal transport. The optimal transport problem is replaced by the Schrödinger problem: an entropy minimization problem on the set of probability measures with marginal constraints. The large deviation principle leading to the Schrödinger problem will be introduced and some easy proofs of functional inequalities, based on this entropy minimization problem, will be sketched.

              News

              King's Mathematician awarded £300,000 Nuffield Grant to study impactful new pension schemes

              The Nuffield Foundation will fund a two year research project in conjunction with the Pension Policy Institute to investigate novel pension schemes

              Money

              King's women in maths: Tiziana Di Matteo

              Tiziana Di Matteo interview

              Tiziana_Di Matteo

              What does COVID-19 mean for the triple lock and State Pension inflation?

              Stochastic simulation models developed by King's mathematicians feature in the Pensions Policy Institute's latest briefing note.

              A glass cup filled with coins and sprouting leaves.

              Events

              28Apr

              Conference on Liquidity Stresses and Financial Stability

              This conference aims to unite leading academics and central bank policymakers to explore critical financial stability challenges.

              12Jul

              London/Oxford/Warwick Financial Mathematics Workshop

              The event will feature talks both established researchers and industry figures and junior researchers

              Please note: this event has passed.

              Seminars

              King's College London Financial Mathematics Seminars

              The Financial Mathematics seminars are held at King’s on Mondays each fortnight. You can find the seminars here.

               

              London Mathematical Finance Group Seminars

              King's College London is a part of the London Mathematical Finance Group which organises the London Mathematical Finance Seminar Series. These seminars will be taking place at UCL.

               

              For more information, please contact: spyridon.pougkakiotis@kcl.ac.uk or purba.das@kcl.ac.uk

              People

              John Armstrong

              Reader in Financial Mathematics

              Cristin Buescu

              Senior Lecturer in Financial Mathematics

              Feiyu Chen

              PhD Student

              James Dalby

              Postdoctoral Research Associate in the Mathematical Modelling of Collective Pensions

              Purba Das

              Lecturer in Financial Mathematics

              Publications

                Activities

                Cristin Buescu
                Recent research on portfolio optimization featured in interview of Dr Cristin Buescu by Faculti.Net

                A comparison of the effectiveness of Machine Learning vs Financial Mathematics techniques when optimally managing a portfolio of cointelated assets was presented in the recent research output of Dr Cristin Buescu, a member of the Financial Mathematics group at King’s.

                City of London
                The Practitioners’ Lecture Series Presents: Antoine Savine

                Workshop: Introduction to back-propagation and automatic adjoint differentiation (AAD) in machine learning and finance, 28-29 March 2019. This six-hour workshop included: Introduction to Artificial Neural Networks and Deep Learning; Back-propagation through ANNs; Applications of Deep Learning in Finance; Hands-on examples with Excel/C++ and Python/Tensor Flow; Extract computation graphs and differentiate arbitrary calculations; Fast (reverse mode) AAD with operator overloading in C++ Application to financial risk management. The Practitioners' Lecture Series at King's College London is organised by Dr Blanka Horvath and sponsored by Simudyne.

                  Graphs
                  FIPS 2018

                  The eighth Workshop on Finance, Insurance, Probability and Statistics (FIPS 2018) brought together a global cast of leading academic experts, practitioners and junior researchers. Attendees shared research that underscored the contributions of probability and statistics to the development of quantitative models, methods, techniques and technologies in the fields of finance and insurance.

                    Graph and equations
                    Risk Management for Whales

                    Thursday, 1 February 2018 Speaker: Lakshithe Wagalath (IESEG School of Management) Title: Risk Management for Whales Abstract: We propose a portfolio risk model which integrates market risk with liquidation costs. The model provides a framework for computing liquidation-adjusted risk measures such as Liquidation-adjusted VaR (LVaR). Calculation of liquidation-adjusted Value-at-Risk (LVaR) for simulated and real-life examples reveals a substantial impact of liquidation costs on portfolio risk for portfolios with large concentrated positions. This is joint work with Rama Cont.

                      London skyline
                      Optimisation in energy markets

                      Optimization in energy markets, 3 April 2017 Speaker 1: Michel De Lara, École des Ponts ParisTech Title: Game Theory with Information: a Framework for the New Energy Systems Speaker 2: Pierre Carpentier, École des Ponts ParisTech Title: Optimization of Energy Production and Transport: Approaches by Decomposition Under Stochasticity Speaker 3: Jean-Philippe Chancelier, École des Ponts ParisTech Title: Stochastic Spatial Decomposition for Large Scale Hydro Valleys Speaker 4: Teemu Pennanen, King's College London Title: Mathematical models for pricing and hedging of delivery contracts

                        City of London skyline
                        Convex Analysis Seminar

                        Convex Analysis Seminar, 30 March 2017 Speaker 1: Ari-Pekka Perkkiö, LMU Mathematics Institute Title: Regular processes and duality Abstract: We study the optional projection on spaces of cadlag and continuous processes. Our main results sharpen those of [Bismut, 1978] in cases where the projected process has additional integrability properties. Moreover, we characterize the topological duals of optional cadlag processes and of regular processes with the given integrability properties. Our main results are derived by purely functional analytic arguments simplifying original proofs of [Bismut, 1978]. We also present results on dual representations for convex integral functionals on regular processes. These yield a maximum principle for a general class of singular stochastic control problems. The talk is based on a joint work with TeemuPennanen. Speaker 2: Christian Léonard, Université Paris Ouest Title: Some results about entropic transport Abstract: Optimal transport is a powerful tool for proving several functional inequalities such as: concentration inequalities, geometric inequalities (Prekopa-Leindler inequality) or entropy-entropy production inequalities related to rates of convergence to equilibrium of heat flows. In this talk, an alternate similar approach will be introduced. It relies on entropic transport rather than standard optimal transport. The optimal transport problem is replaced by the Schrödinger problem: an entropy minimization problem on the set of probability measures with marginal constraints. The large deviation principle leading to the Schrödinger problem will be introduced and some easy proofs of functional inequalities, based on this entropy minimization problem, will be sketched.

                          News

                          King's Mathematician awarded £300,000 Nuffield Grant to study impactful new pension schemes

                          The Nuffield Foundation will fund a two year research project in conjunction with the Pension Policy Institute to investigate novel pension schemes

                          Money

                          King's women in maths: Tiziana Di Matteo

                          Tiziana Di Matteo interview

                          Tiziana_Di Matteo

                          What does COVID-19 mean for the triple lock and State Pension inflation?

                          Stochastic simulation models developed by King's mathematicians feature in the Pensions Policy Institute's latest briefing note.

                          A glass cup filled with coins and sprouting leaves.

                          Events

                          28Apr

                          Conference on Liquidity Stresses and Financial Stability

                          This conference aims to unite leading academics and central bank policymakers to explore critical financial stability challenges.

                          12Jul

                          London/Oxford/Warwick Financial Mathematics Workshop

                          The event will feature talks both established researchers and industry figures and junior researchers

                          Please note: this event has passed.

                          Seminars

                          King's College London Financial Mathematics Seminars

                          The Financial Mathematics seminars are held at King’s on Mondays each fortnight. You can find the seminars here.

                           

                          London Mathematical Finance Group Seminars

                          King's College London is a part of the London Mathematical Finance Group which organises the London Mathematical Finance Seminar Series. These seminars will be taking place at UCL.

                           

                          For more information, please contact: spyridon.pougkakiotis@kcl.ac.uk or purba.das@kcl.ac.uk