scenario trees/lattice

[msz13]

Scenario trees/lattice reading

Scenarios for multistage stochastic programs
https://www.karlin.mff.cuni.cz/~kopa/papers/vanc-ed.pdf

Overview of scenario tree generation methods, applied in financial and economic decision making
https://www.semanticscholar.org/paper/Overview-of-scenario-tree-generation-methods%2C-in-V%C3%A1zsonyi/70242b4d448621b2e2b7b4833a7d912dbd4c5a65

Problem-Driven Scenario Clustering in Stochastic Optimization
https://arxiv.org/pdf/2106.11717.pdf

Scenario tree generation approaches using K-means and LP moment matching methods
https://www.sciencedirect.com/science/article/pii/S0377042712002300

StochOptim
https://github.com/julienkeutchayan/StochOptim/tree/master

Multistage K-Means Clustering for Scenario Tree Construction
https://informatica.vu.lt/journal/INFORMATICA/article/579/info

Dynamic Tree Generation
https://www-user.tu-chemnitz.de/~alopi/publications/DynamicTreeGen.pdf

Problem driven scenaro tree generation
https://www.mdpi.com/1999-4893/16/10/479

Scenario sampling
https://www.researchgate.net/publication/317845601_Comparison_of_Sampling_Methods_for_Dynamic_Stochastic_Programming

Finite-State Markov-Chain Approximations: A Hidden Markov Approach
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4137592
Inna wersja
https://congress-files.s3.amazonaws.com/2022-07/SSRN_20220615.pdf

The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2780166

Importence Sampling
https://www.researchgate.net/publication/276162840_Importance_Sampling_in_Stochastic_Programming_A_Markov_Chain_Monte_Carlo_Approach

Simulation and optimization approaches to scenario tree generation
https://www.sciencedirect.com/science/article/abs/pii/S0165188903001131

New Algorithms And Fast Implementations To Approximate Stochastic Processes
https://www.researchgate.net/publication/346578092_New_Algorithms_And_Fast_Implementations_To_Approximate_Stochastic_Processes

Aggregation and Discretization in Multistage Stochastic Programming
https://edoc.hu-berlin.de/bitstream/handle/18452/8999/18.pdf?sequence=1

Performance comparison of scenario generation methods applied to a stochastic optimization asset-liability_management_model
https://www.researchgate.net/publication/324522700_Performance_comparison_of_scenario-generation_methods_applied_to_a_stochastic_optimization_asset-liability_management_model

Optimisation of Stochastic Programming by Hidden Markov Modelling based Scenario Generation
https://www.researchgate.net/publication/46461932_Optimisation_of_Stochastic_Programming_by_Hidden_Markov_Modelling_based_Scenario_Generation

A Parsimonious Model for Generating Arbitrage-Free Scenario Trees
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362014

Scenario tree modelling for multistage stochastic programs
https://www.wias-berlin.de/people/heitsch/HR05svjour.pdf

Adaptive lattice methods for multi-asset models
https://core.ac.uk/download/pdf/82640129.pdf

Experimental Study of Methods of Scenario Lattice Construction for Stochastic Dual Dynamic Programming - Scenario Lattice
https://www.scirp.org/journal/paperinformation?paperid=110139

Gas Storage Valuation in Incomplete Markets - single variable, lattice discretisation
https://www.researchgate.net/publication/341743003_Gas_Storage_Valuation_in_Incomplete_Markets

Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2585859

Discretization of the Markov Regime Switching AR(1) Process
http://www.liuyanecon.com/wp-content/uploads/MRS-Discretization.pdf

Foreign exchange trading and management with the stochastic dual dynamic programming method (transform AR(1) to gbm)
https://jfin-swufe.springeropen.com/articles/10.1186/s40854-022-00433-7

Evaluation of Scenario-Generation Methods for Stochastic Programming
https://www.researchgate.net/publication/2837745_Evaluation_of_Scenario-Generation_Methods_for_Stochastic_Programming

Scenario Reduction in Stochastic Programming: An Approach Using Probability Metrics
https://www.researchgate.net/publication/243784656_Scenario_Reduction_in_Stochastic_Programming_An_Approach_Using_Probability_Metrics

Problem driven articles
https://github.com/julienkeutchayan/StochOptim

Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure
https://www.researchgate.net/publication/337553023_Problem-driven_scenario_generation_an_analytical_approach_for_stochastic_programs_with_tail_risk_measure
Discretization

Performance comparison of scenario-generation methods applied to a stochastic optimization asset-liability management model
https://www.researchgate.net/publication/324522700_Performance_comparison_of_scenario-generation_methods_applied_to_a_stochastic_optimization_asset-liability_management_model

https://alexisakira.github.io/discretization/

The Discretization Filter: A Simple Way to Estimate Nonlinear State Space Models
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2780166

Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2585859

A new method for approximating vector autoregressive processes by finite-state Markov chains
https://www.researchgate.net/publication/241765539_A_new_method_for_approximating_vector_autoregressive_processes_by_finite-state_Markov_chains

[msz13]

TODO:

1. Tylko kemans

• symulacja dla całego okresu
• obliczenie klastrów i prawdopodobieńst dla jednego okresu - dane zdenormalizowane
• obliczenie klastrów i prawdopodobieńst dla wszystkich okresow
• zapisanie scenario lattice
• momenty poszczegolnych klas aktywow i okresów

2. Kmeans z moments

• oblicz momenty dla scenariuszy należących do początkowego klastra
• oblicz prawdopodobienstwa, do momentow i kmeans
• cala funkcja dla wzystkich i okresow
• porownaj wartosc funkcji obiejtywnej dla róznych ilości nodes

3. NA później

• wczytaj model(parametry) - z pliku

[msz13]

scenario: calculate probs for scenarios
given clusters [1 1 2 3 3 2 2 1] statege one
and  second stage clusters [2 1 3 2 3 3 1 1 ]
when calculate probs
than probs per node
| node 1 | node 2 | prob |
| 1 |  1 | 2/3 |
| 1 | 2 | 1/3 |
| 2 |  1 | 1/3 |
| 2 | 3 | 2/3 |
| 3 |  2 | 1/2 |
| 3 |  3 | 1/2 |