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Introduction
Current institution
Publications
Publications (148)
We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic i...
We analyze the investment behavior of private clients with regard to retail structured products. To ascertain their stated and revealed preferences, we use a questionnaire and a field experiment. The real product issued in the field experiment is comparable to the hypothetical product in the questionnaire in terms of both payoff and communication....
We propose a simple model of credit contagion in which we include macro- and microstructural interdependencies among the debtors within a credit portfolio. The microstructure captures interdependencies between debtors that go beyond their exposure to common factors, e.g., business or legal interdependencies. We show that even for diversified portfo...
These lecture notes cover old and new investment methods, regulatory and legal developments and the role of technology as a game changer in asset management.
The discussion gives the same weight to the theoretical and practical aspects of asset management.
The focus is on portfolio constructions, asset pricing foundations, factor investing and ba...
Online banking fraud occurs whenever a criminal can seize accounts and transfer funds from an individual’s online bank account. Successfully preventing this requires the detection of as many fraudsters as possible, without producing too many false alarms. This is a challenge for machine learning owing to the extremely imbalanced data and complexity...
To address the tragedy of the horizon, carbon emissions must be priced and companies' long-term climate goals must be aligned with their short-term planning process. Our model shows how long-term climate risks can be integrated into short-term management decisions using a Carbon Risk Budgeting Process (CRBP). The CRBP indicates how much risk budget...
We define such a process using three interdependent models: Machine-learning based fraud detection, economic optimization of the machine learning outputs, and a risk model for risk predictions based on the optimized machine learning outputs. The results of the risk simulation for three payment channels, based on real fraud and non-fraud data, show...
Buildings account for between 20 and 40 percent of greenhouse gas emissions worldwide. Most countries have set long-term emission reduction targets ("net zero paths").
We show that asset-backed security wrappers on energy performance contracts significantly enable the achievement of net-zero targets: the renovation rate can be increased to almost...
We discuss the challenges of decision-making in the Covid 19 pandemic. The focus is on the volume of information and misinformation, the interplay of science and government, and the uncertainties and complexities of decision-making. Scientific illiteracy, inequalities in vaccination across the globe, the effective containment of misinformation, the...
The current COVID-19 pandemic clarifies that protecting health, the health system, and the economy are linked. We discuss why the decision-making situation for measures in the first phase of the epidemics is much easier than for the second phase. Guidelines of successful health and economic policy in the first and second phases impact the risk asse...
Content Complex Analysis:
Complex numbers,
Holomorphic functions,
Power series,
Multi-valued functions,
Theorems of integration theory (Theorems of Cauchy and the Residue Theorem),
Content Fourier analysis:
Approximation theory for continuous functions,
Approximation in the mean-square sense,
Pointwise and uniform convergence of Fourier...
Complex Analysis
Complex numbers: holomorphic functions, power series, multi-valued functions, the classic theorem of integration theory (Theorems of Cauchy and the Residue Theorem).
Fourier analysis: Approximation theory for continuous functions, approximation in the mean-square
sense, i.e. Hilbert space theory, pointwise and uniform convergence...
0.1 Motivation,
0.2 Introduction to Option Pricing,
0.3 Formal Option Pricing Calculation,
0.4 Regularity of the Characteristic Function,
0.5 Variance Gamma Model,
0.6 Simplified Stochastic Volatility Model,
0.7 Lewis' Option Pricing Formula
0.1 Overview
0.2 Projection - Intuition
0.3 Projection Operators
0.4 Geometry of Orthogonal Projections
0.5 Projections Expressed in Basis Vectors
0.6 Quadratic Optimization
0.1 Overview
0.2 Bounded Operators on Hilbert Spaces
0.3 Adjoint Operators on Hilbert Spaces
0.4 Adjoint Operators on Normed Spaces
Riemann vs. Lebesgue
Integration Theorems of Monotone Convergence, Lebesgue, Fatou and Fubini
We discuss contingent and financial market equilibrium models. We favour
simplicity over generality. This means we restrict to one-period models and
agent's preferences are assumed to be smooth functions. Existence is one
key issue which relates to the fix point theorem of Brouwer and effciency of
equilibria in complete and incomplete financial mar...
We provide an introduction to statistical learnings theory (SLT). We first
motivate SLT and consider consistency and the estimation error. We
encounter the inequalities of Chernoof and Hoefding and prove the
fundamental results of Vapnik and Chervonenkis is SLT.
Lemma of Sard
Brouwer Fixed Point Theorem
Transversality Theorem, Part 2
Homotopy
Degree
Intersection Number, Lefschetz Fixed Point Theorem
Manifolds
Tangent Space
Maps between Manifolds
Implicit Function Theorem in Rn
Implicit Function Theorem on Manifolds
Transversality
1. Positive operators and polar decompositioon
2. Schatten class operators
3. Trace class operators
4. Hilbert-Schmidt operators
5. Determinant function on Hilbert Spaces
We start with the analytic Fredholm Alternative which has the Fredholm
Alternative, the Riesz-Schauder Theorem, the Hilbert-Schmidt Theorem
and the Canonical Representation of Compact Operators as consequences.
The next sections consider application of the theory: Integral equations
of the second kind, Fredholm theory, Integral equations
of the sec...
Spectral theory
Resolvent calculus
Examples: Multiplication Operator, Shift Operators
Compact operators
0.1 Overview
0.2 Simple General Equilibrium Model
0.3 Fundamental Asset Pricing Equation
0.4 Fundamental Asset Pricing Equation in Traditional Notation
0.4.1 Examples; 0.4.2 Relationship between Factor Models and Beta Representations
Digital disruption changes the financial industry far more widely than the regulatory avalanches
did since the financial crisis 2008: The business model in the near future is the digital business
model. This triggers the question of production ownership and customer relationship ownership.
Can new entrants such as Fintech or the tech giants replace...
We introduce to bounded operators and projection operators on infinite dimensional spaces. We apply the methods to the Markowitz model quadratic optimization problems.
Brownian motion (BM) is a basic stochastic process in mathematics, economics and finance. We explain the construction of Brownian motion, some if its properties and the construction of the integral w.r.t. BM. The approach is semi-complete, i.e. it is more detailed than usual applied lectures but does not go into full details of measure theory.
Related to the stochastic integral w.r.t. BM there is a suggestive stochastic differential calculus which is used to model the stochastic time evolution of prices, rates, etc. in the form of stochastic differential equations (SDE). We introduce to this calculus, discuss the central change of variable formula (Itô's Lemma) and several applications o...
Brownian motion (BM) is a basic stochastic process in mathematics, economics and finance. We explain the construction of Brownian motion, some if its properties and the construction of the integral w.r.t. BM. The approach is semi-complete, i.e. it is more detailed than pure applied approached but less complete than a full mathematical treatment.
0.1 Motivation,
0.2 Damped Fourier Theory of Carr and Madan,
0.3 The Fourier - and Inverse Fourier transform for a > 0,
0.4 Pricing independent of specific damping values a.
0.1 Overview
0.2 Holomorphic Functions
0.3 Integral Theorem of Cauchy
This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2015. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss the past and current developments and necessary next steps for dealing with old-age provision. Topics include the pension funding gap, d...
This paper analyzes structured products with a focus on the Swiss market. Empirical results for these products’ five major categories are presented, along with case studies and a general discussion. The paper addresses three main questions: How did structured products perform in the period starting in the Great Financial Crisis 2008 until 2014? The...
We describe and analyze the asset pricing, technology and regulatory changes in the banking sector.
The material is structured as follows:
1. Asset pricing. We start with the benchmark of perfect and complete markets. We first extend to incomplete and imperfect markets and second, to asset pricing with counter party risk in OTC derivatives, with...
We describe and analyze the asset pricing, technology and regulatory changes in the banking sector.
The material is structured as follows:
1. Asset pricing. We start with the benchmark of perfect and complete markets. We first extend to incomplete and imperfect markets and second, to asset pricing with counter party risk in OTC derivatives, with...
Retail client investment business faces decreasing profitability. The regulatory changes add further complexity, risks and costs to the business. In order to remain profitable and to control conduct-of-business risks, the business model has to be redesigned. We propose a mandate solution which envelops traditional investment fund type mandates. The...
Investment business for private clients faces a challenging environment. Profitability is decreasing due to competition and regulatory complexity. To remain profitable and control business risks, the business models have to be redesigned. We propose a solution based on automatization and the reduction of business risk such as poor performance, wron...
These lecture notes are about financial innovations. We ask why are there some innovation and how is an innovative idea realized. This forces us to consider practical and structural aspects (regulations, taxation, markets) as key drivers of innovations and also basic formal aspects in valuation. The notes are taken from lectures to master students...
We study the partial and general equilibrium implications of value-at-risk (VaR) regulation in continuous-time economies with intermediate expenditure, stochastic opportunity set, and heterogeneous attitudes to risk. Our findings show that because of an anticipatory effect of VaR constraints on the optimal hedging demand, the partial equilibrium in...
Market frictions inhibit the perfect replication of property derivatives, and define the property spread as a price measure
in the incomplete real estate market. We identify transaction costs, transaction time, and short sale constraints as the main
frictions in this market. Based on these frictions, we set up a framework of arbitrage free price bo...
We study the optimal policies and mean-variance frontiers (MVF) of a multiperiod mean-variance optimization of assets and liabilities (AL). This makes the analysis more challenging than for a setting based on purely exogenous liabilities, in which the optimization is only performed on the assets while keeping liabilities fixed. We show that, under...
We consider the fime value of money, the construction of term structures, no arbitrage pricing theory in the one-period, multi-period and continuous time setup, bonds, short rate and LIBOR market models, convertible bonds and introduce to systemic risk focusing on debt markets.
Lecture Notes in risk transfer and risk management. The notes consider capital protecting structured note investments for the equity, FX, interest rate and weather asset class. We discuss capital protected investment for pension funds and the construction of capital protection without option markets and its relation to CPPI.
We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive relationships between the different concepts. The relationships are of an exact analytical type if this is possible, else we use expansions to obtain approximate expressions. We close with a discussion of the mixing theorem.
We analyze the investment behavior of private clients with regard to structured products. To
ascertain their stated and revealed preferences, we use a questionnaire and a field experiment.
The real product issued in the field experiment is comparable to the hypothetical product in
the questionnaire in terms of both payoff and communication. We find...
We recall some fundamentals on Levy processes. Then the Gamma distribution, the Variance Gamma process and Option pricing for this process are considered in detail. To implement the model we provide an analysis using the fast Fourier transform applied to option pricing, time change and to error bounds for the Variance Gamma model.
We consider the modelling of credit migration risk and the pricing of migration
derivatives. To construct a Point-in-Time (PIT) rating migration matrix as the underlying
value for derivative pricing we show first that the Affine Markov Chain models is
not sufficient to generate PIT migration matrices in both, an economic boom and contraction.
We sh...
We consider in these lecture notes analytical topics of the Heston model. Mathematical methods such as Fourier theory, complex analysis, generalized functions and partial differential equations are discussed. To make these theories accessible to students with a standard economic or finance background, we stress intuition and explicit calculations.
The recent real estate bubble was fuelled by non-risk-adjusted lending policies, low interest rates, and complex finance vehicles. Mortgage-backed securities (MBS) played a crucial role in the crisis. These vehicles were praised as liquid capital market instruments that allowed mortgage lenders to replenish their funds, which could then be used for...
