4,568 research outputs found
Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization
We introduce a regularization approach to arbitrage-free factor-model
selection. The considered model selection problem seeks to learn the closest
arbitrage-free HJM-type model to any prespecified factor-model. An asymptotic
solution to this, a priori computationally intractable, problem is represented
as the limit of a 1-parameter family of optimizers to computationally tractable
model selection tasks. Each of these simplified model-selection tasks seeks to
learn the most similar model, to the prescribed factor-model, subject to a
penalty detecting when the reference measure is a local martingale-measure for
the entire underlying financial market. A simple expression for the penalty
terms is obtained in the bond market withing the affine-term structure setting,
and it is used to formulate a deep-learning approach to arbitrage-free affine
term-structure modelling. Numerical implementations are also performed to
evaluate the performance in the bond market.Comment: 23 Pages + Reference
Modelling of tradeable securities with dividends
We propose a generalized framework for the modeling of tradeable securities with dividends
which are not necessarily cash dividends at fixed times or continuously paid dividends. In our
setup the dividend processes are only required to be semi-martingales. We give a definition of
self-financing replication which incorporates dividend processes, and we show how this allows
us to translate standard results for the pricing and hedging of derivatives on assets without
dividends to the case of assets with dividends. We then apply this framework to analyze and
compare the different assumptions that have been made in earlier dividend models. We also
study the case where we have uncertain dividend dates, and we look at securities which are
not equity-based such as futures and credit default swaps, since our weaker assumptions on
the dividend process allow us to consider these other applications as well
Convertible Bonds: Default Risk and Uncertain Volatility
Within a default intensity approach we discuss the optimal exercise of the callable and convertible bonds. Pricing bounds for convertible bonds are derived in an uncertain volatility model, i.e. when the volatility of the stock price process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk
A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting
We present a version of the fundamental theorem of asset pricing (FTAP) for
continuous time large financial markets with two filtrations in an
-setting for . This extends the results of Yuri
Kabanov and Christophe Stricker \cite{KS:06} to continuous time and to a large
financial market setting, however, still preserving the simplicity of the
discrete time setting. On the other hand it generalizes Stricker's
-version of FTAP \cite{S:90} towards a setting with two filtrations. We do
neither assume that price processes are semi-martigales, (and it does not
follow due to trading with respect to the \emph{smaller} filtration) nor that
price processes have any path properties, neither any other particular property
of the two filtrations in question, nor admissibility of portfolio wealth
processes, but we rather go for a completely general (and realistic) result,
where trading strategies are just predictable with respect to a smaller
filtration than the one generated by the price processes. Applications range
from modeling trading with delayed information, trading on different time
grids, dealing with inaccurate price information, and randomization approaches
to uncertainty
Pairs Trading under Drift Uncertainty and Risk Penalization
In this work, we study a dynamic portfolio optimization problem related to
pairs trading, which is an investment strategy that matches a long position in
one security with a short position in another security with similar
characteristics. The relationship between pairs, called a spread, is modeled by
a Gaussian mean-reverting process whose drift rate is modulated by an
unobservable continuous-time, finite-state Markov chain. Using the classical
stochastic filtering theory, we reduce this problem with partial information to
the one with full information and solve it for the logarithmic utility
function, where the terminal wealth is penalized by the riskiness of the
portfolio according to the realized volatility of the wealth process. We
characterize optimal dollar-neutral strategies as well as optimal value
functions under full and partial information and show that the certainty
equivalence principle holds for the optimal portfolio strategy. Finally, we
provide a numerical analysis for a toy example with a two-state Markov chain.Comment: 24 pages, 4 figure
Utility-Based Hedging of Stochastic Income
In this dissertation, we study and examine utility-based hedging of the optimal portfolio choice problem in stochastic income. By assuming that the investor has a preference governed by negative exponential utility, we a derive a closed-form solution for the indifference price through the pricing methodology based on utility maximization criteria. We perform asymptotic analysis on this closed form solution to develop the analytic approximation for the indifference price and the optimal hedging strategy as a power series expansion involving the risk aversion and the correlation between the income and a traded asset. This gives a fast computation route to assess these quantities and perform our analysis. We implemented the model to perform simulations for the optimal hedging policy and produce the distributions of the hedging error at terminal time over many sample paths histories. In turn, we analyze the performance of the utility-based hedging strategy together with the strategy which arises from employing the traded asset as a substitute for the stochastic income
Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty
We study robust stochastic optimization problems in the quasi-sure setting in
discrete-time. The strategies in the multi-period-case are restricted to those
taking values in a discrete set. The optimization problems under consideration
are not concave. We provide conditions under which a maximizer exists. The
class of problems covered by our robust optimization problem includes optimal
stopping and semi-static trading under Knightian uncertainty.Comment: arXiv admin note: text overlap with arXiv:1610.0923
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