4,902 research outputs found
From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments
We consider a non-stochastic online learning approach to price financial
options by modeling the market dynamic as a repeated game between the nature
(adversary) and the investor. We demonstrate that such framework yields
analogous structure as the Black-Scholes model, the widely popular option
pricing model in stochastic finance, for both European and American options
with convex payoffs. In the case of non-convex options, we construct
approximate pricing algorithms, and demonstrate that their efficiency can be
analyzed through the introduction of an artificial probability measure, in
parallel to the so-called risk-neutral measure in the finance literature, even
though our framework is completely adversarial. Continuous-time convergence
results and extensions to incorporate price jumps are also presented
Optimal Dynamic Portfolio with Mean-CVaR Criterion
Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk
measures from academic, industrial and regulatory perspectives. The problem of
minimizing CVaR is theoretically known to be of Neyman-Pearson type binary
solution. We add a constraint on expected return to investigate the Mean-CVaR
portfolio selection problem in a dynamic setting: the investor is faced with a
Markowitz type of risk reward problem at final horizon where variance as a
measure of risk is replaced by CVaR. Based on the complete market assumption,
we give an analytical solution in general. The novelty of our solution is that
it is no longer Neyman-Pearson type where the final optimal portfolio takes
only two values. Instead, in the case where the portfolio value is required to
be bounded from above, the optimal solution takes three values; while in the
case where there is no upper bound, the optimal investment portfolio does not
exist, though a three-level portfolio still provides a sub-optimal solution
Market models with optimal arbitrage
We construct and study market models admitting optimal arbitrage. We say that
a model admits optimal arbitrage if it is possible, in a zero-interest rate
setting, starting with an initial wealth of 1 and using only positive
portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is
the strategy for which this constant has the highest possible value. Our
definition of optimal arbitrage is similar to the one in Fernholz and Karatzas
(2010), where optimal relative arbitrage with respect to the market portfolio
is studied. In this work we present a systematic method to construct market
models where the optimal arbitrage strategy exists and is known explicitly. We
then develop several new examples of market models with arbitrage, which are
based on economic agents' views concerning the impossibility of certain events
rather than ad hoc constructions. We also explore the concept of fragility of
arbitrage introduced in Guasoni and Rasonyi (2012), and provide new examples of
arbitrage models which are not fragile in this sense
Hedging Against the Interest-rate Risk by Measuring the Yield-curve Movement
By adopting the polynomial interpolation method, we propose an approach to
hedge against the interest-rate risk of the default-free bonds by measuring the
nonparallel movement of the yield-curve, such as the translation, the rotation
and the twist. The empirical analysis shows that our hedging strategies are
comparable to traditional duration-convexity strategy, or even better when we
have more suitable hedging instruments on hand. The article shows that this
strategy is flexible and robust to cope with the interest-rate risk and can
help fine-tune a position as time changes.Comment: 12 pages, 2 tables, 5 figure
The maximum maximum of a martingale with given marginals
We obtain bounds on the distribution of the maximum of a martingale with
fixed marginals at finitely many intermediate times. The bounds are sharp and
attained by a solution to -marginal Skorokhod embedding problem in
Ob{\l}\'oj and Spoida [An iterated Az\'ema-Yor type embedding for finitely many
marginals (2013) Preprint]. It follows that their embedding maximizes the
maximum among all other embeddings. Our motivating problem is superhedging
lookback options under volatility uncertainty for an investor allowed to
dynamically trade the underlying asset and statically trade European call
options for all possible strikes and finitely-many maturities. We derive a
pathwise inequality which induces the cheapest superhedging value, which
extends the two-marginals pathwise inequality of Brown, Hobson and Rogers
[Probab. Theory Related Fields 119 (2001) 558-578]. This inequality, proved by
elementary arguments, is derived by following the stochastic control approach
of Galichon, Henry-Labord\`ere and Touzi [Ann. Appl. Probab. 24 (2014)
312-336].Comment: Published at http://dx.doi.org/10.1214/14-AAP1084 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Empirical tests of a simple pricing model for sugar futures
Price Theory;Estimation
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.
Quantum Model Averaging
Standard tomographic analyses ignore model uncertainty. It is assumed that a
given model generated the data and the task is to estimate the quantum state,
or a subset of parameters within that model. Here we apply a model averaging
technique to mitigate the risk of overconfident estimates of model parameters
in two examples: (1) selecting the rank of the state in tomography and (2)
selecting the model for the fidelity decay curve in randomized benchmarking.Comment: For a summary, see http://i.imgur.com/nMJxANo.pn
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