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Finite Horizon Portfolio Selection
We study the problem of maximising expected utility of terminal wealth
over a nite horizon, with one risky and one riskless asset available, and
with trades in the risky asset subject to proportional transaction costs.
In a discrete time setting, using a utility function with hyperbolic risk
aversion, we prove that the optimal trading strategy is characterised by
a function of time (t), which represents the ratio of wealth held in the
risky asset to that held in the riskless asset. There is a time varying no
transaction region with boundaries b(t) < s(t), such that the portfo-
lio is only rebalanced when (t) is outside this region. The results are
consistent with similar studies of the in nite horizon problem with in-
termediate consumption, where the no transaction region has a similar,
but time independent, characterisation. We solve the problem numerically
and compute the boundaries of the no transaction region for typical model
parameters. We show how the results can be used to implement option
pricing models with transaction costs based on utility maximisation over
a nite horizo
Optimal Execution with Dynamic Order Flow Imbalance
We examine optimal execution models that take into account both market
microstructure impact and informational costs. Informational footprint is
related to order flow and is represented by the trader's influence on the flow
imbalance process, while microstructure influence is captured by instantaneous
price impact. We propose a continuous-time stochastic control problem that
balances between these two costs. Incorporating order flow imbalance leads to
the consideration of the current market state and specifically whether one's
orders lean with or against the prevailing order flow, key components often
ignored by execution models in the literature. In particular, to react to
changing order flow, we endogenize the trading horizon . After developing
the general indefinite-horizon formulation, we investigate several tractable
approximations that sequentially optimize over price impact and over . These
approximations, especially a dynamic version based on receding horizon control,
are shown to be very accurate and connect to the prevailing Almgren-Chriss
framework. We also discuss features of empirical order flow and links between
our model and "Optimal Execution Horizon" by Easley et al (Mathematical
Finance, 2013).Comment: 31 pages, 8 figure
Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models
The recently introduced class of simultaneous graphical dynamic linear models
(SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting
to higher-dimensional time series. This paper advances the methodology of
SGDLMs, developing and embedding a novel, adaptive method of simultaneous
predictor selection in forward filtering for on-line learning and forecasting.
The advances include developments in Bayesian computation for scalability, and
a case study in exploring the resulting potential for improved short-term
forecasting of large-scale volatility matrices. A case study concerns financial
forecasting and portfolio optimization with a 400-dimensional series of daily
stock prices. Analysis shows that the SGDLM forecasts volatilities and
co-volatilities well, making it ideally suited to contributing to quantitative
investment strategies to improve portfolio returns. We also identify
performance metrics linked to the sequential Bayesian filtering analysis that
turn out to define a leading indicator of increased financial market stresses,
comparable to but leading the standard St. Louis Fed Financial Stress Index
(STLFSI) measure. Parallel computation using GPU implementations substantially
advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table
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