12,094 research outputs found
A Literature Review: Modelling Dynamic Portfolio Strategy under Defaultable Assets with Stochastic Rate of Return, Rate of Inflation and Credit Spread Rate
This research aims to find an optimal solution for dynamic portfolio in finite-time horizon under defaultable assets, which means that the assets has a chance to be liquidated in a finite time horizon, e.g corporate bond. Besides investing on those assets, investors will also have benefit in the form of consumption. As a reference in making investment decisions the concept of utility functions and volatility will play a role. Optimal portfolio composition will be obtained by maximizing the total expected discounted utility of consumption in the time span during the investment is executed and also to minimize the risk, the volatility of the investment. Further the reduced form model is applied since the assets prices can be linked with the market risk and the credit risk. The interest rate and the rate of inflation will be allowed as a representation of market risk, while the credit spread will be used as a representation of credit risk. The dynamic of asset prices can be derived analytically by using Ito Calculus in the form of the movement of the three risk factors above. Furthermore, this problem will be solved using the stochastic dynamic programming method by assuming that market is incomplete. Depending on the chosen utility function, the optimal solution of the portfolio composition and the consumption can be found explicitly in the form of feedback control. This is possible since the dynamic of the wealth process of the control variable is linear. To apply dynamic programming as well as to find solutions we use Backward Stochastic Differential Equation (BSDE) where the solution can be solved explicitly, especially where the terminal value of the investment target is chosen random. Further, it will be modeled with Monte Carlo simulation and, calibrated using Indonesia data of stock and corporate bond
Sequential Monte Carlo pricing of American-style options under stochastic volatility models
We introduce a new method to price American-style options on underlying
investments governed by stochastic volatility (SV) models. The method does not
require the volatility process to be observed. Instead, it exploits the fact
that the optimal decision functions in the corresponding dynamic programming
problem can be expressed as functions of conditional distributions of
volatility, given observed data. By constructing statistics summarizing
information about these conditional distributions, one can obtain high quality
approximate solutions. Although the required conditional distributions are in
general intractable, they can be arbitrarily precisely approximated using
sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes,
is potentially heavy computational demand. We present two variants of the
algorithm, one closely related to the well-known least-squares Monte Carlo
algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001)
113-147], and the other solving the same problem using a "brute force" gridding
approach. We estimate an illustrative SV model using Markov chain Monte Carlo
(MCMC) methods for three equities. We also demonstrate the use of our algorithm
by estimating the posterior distribution of the market price of volatility risk
for each of the three equities.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS286 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamic programming approach to principal-agent problems
We consider a general formulation of the Principal-Agent problem with a
lump-sum payment on a finite horizon, providing a systematic method for solving
such problems. Our approach is the following: we first find the contract that
is optimal among those for which the agent's value process allows a dynamic
programming representation, for which the agent's optimal effort is
straightforward to find. We then show that the optimization over the restricted
family of contracts represents no loss of generality. As a consequence, we have
reduced this non-zero sum stochastic differential game to a stochastic control
problem which may be addressed by the standard tools of control theory. Our
proofs rely on the backward stochastic differential equations approach to
non-Markovian stochastic control, and more specifically, on the recent
extensions to the second order case
Portfolio Choice with Stochastic Investment Opportunities: a User's Guide
This survey reviews portfolio choice in settings where investment
opportunities are stochastic due to, e.g., stochastic volatility or return
predictability. It is explained how to heuristically compute candidate optimal
portfolios using tools from stochastic control, and how to rigorously verify
their optimality by means of convex duality. Special emphasis is placed on
long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure
Optimal market making under partial information with general intensities
Starting from the Avellaneda–Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones under full information, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewise-deterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the market maker needs to adjust for additional regime uncertainty in terms of P&L sensitivity and observed order flow volatility. This effect becomes higher, the longer the waiting time in between orders
Mild solutions to the dynamic programming equation for stochastic optimal control problems
We show via the nonlinear semigroup theory in that the
-D dynamic programming equation associated with a stochastic optimal control
problem with multiplicative noise has a unique mild solution with . The -dimensional case is also investigated
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