420,274 research outputs found
Set optimization - a rather short introduction
Recent developments in set optimization are surveyed and extended including
various set relations as well as fundamental constructions of a convex analysis
for set- and vector-valued functions, and duality for set optimization
problems. Extensive sections with bibliographical comments summarize the state
of the art. Applications to vector optimization and financial risk measures are
discussed along with algorithmic approaches to set optimization problems
Evolutionary multi-stage financial scenario tree generation
Multi-stage financial decision optimization under uncertainty depends on a
careful numerical approximation of the underlying stochastic process, which
describes the future returns of the selected assets or asset categories.
Various approaches towards an optimal generation of discrete-time,
discrete-state approximations (represented as scenario trees) have been
suggested in the literature. In this paper, a new evolutionary algorithm to
create scenario trees for multi-stage financial optimization models will be
presented. Numerical results and implementation details conclude the paper
A Comparative Study on the Use of Classification Algorithms in Financial Forecasting
Financial forecasting is a vital area in computational finance, where several studies have taken place over the years. One way of viewing financial forecasting is as a classification problem, where the goal is to find a model that represents the predictive relationships between predictor attribute values and class attribute values. In this paper we present a comparative study between two bio-inspired classification algorithms, a genetic programming algorithm especially designed for financial forecasting, and an ant colony optimization one, which is designed for classification problems. In addition, we compare the above algorithms with two other state-of-the-art classification algorithms, namely C4.5 and RIPPER. Results show that the ant colony optimization classification algorithm is very successful, significantly outperforming all other algorithms in the given classification problems, which provides insights for improving the design of specific financial forecasting algorithms
A note on evolutionary stochastic portfolio optimization and probabilistic constraints
In this note, we extend an evolutionary stochastic portfolio optimization
framework to include probabilistic constraints. Both the stochastic
programming-based modeling environment as well as the evolutionary optimization
environment are ideally suited for an integration of various types of
probabilistic constraints. We show an approach on how to integrate these
constraints. Numerical results using recent financial data substantiate the
applicability of the presented approach
Investment Optimization under Constraints
We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some ``imperfection'', such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002), Long (2002). We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999).Stochastic Optimization, Investment Optimization, Duality Theory, Convex and State Constraints, Optional Decomposition
Multistage Portfolio Optimization: A Duality Result in Conic Market Models
We prove a general duality result for multi-stage portfolio optimization
problems in markets with proportional transaction costs. The financial market
is described by Kabanov's model of foreign exchange markets over a finite
probability space and finite-horizon discrete time steps. This framework allows
us to compare vector-valued portfolios under a partial ordering, so that our
model does not require liquidation into some numeraire at terminal time.
We embed the vector-valued portfolio problem into the set-optimization
framework, and generate a problem dual to portfolio optimization. Using recent
results in the development of set optimization, we then show that a strong
duality relationship holds between the problems
General Smooth Solutions to the HJB PDE: Applications to Finance
We overcome a major obstacle in mathematical optimization. In so doing, we
provide a smooth solution to the HJB PDE without assuming the differentiability
of the value function. We apply our method to financial models
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