La segunda pregunta la divido en tres partes:

Mathematical programming is used to quantify the effect of tax on investments, capital flows and arbitrage. By using proposed models, the impact of taxes on private portfolio optimization, global market performance and asset pricing are investigated. The experimental results demonstrate the importance of tax in all three fields and provide some useful conclusions for investors and governments.

6.1 Personal Investment Tax in Portfolio Optimization

In Chapter 3, to investigate the impact of personal investment taxes on private portfolio optimization, a post-tax portfolio optimization model with integer-based trading constraints is developed. In order to examine the real influence of income tax on portfolio management, many real-world trading constraints are considered. These include the need for diversification, requirements on both the number of assets in a portfolio and the maximum holdings in single assets, round-lot buying, and taxation on cash withdrawals (the last two are modeled with integer variables). The proposed model also accounts for the risk in estimating expected asset returns through the introduction of a stochastic constraint, by which the expected return of the portfolio exceeds the threshold with a high confidence level.

One key contribution of this thesis is that it innovates on the basic Greedy algorithm, making it available for post-tax portfolio optimization problems in which stochastic risk and real-life market restrictions modelled with integer constraints are simultaneously considered. The combination of integer and nonlinear constraints reflects the complexity involved in solving such problems under large-scale applications for which very few solvers are efficient. The efficacy of the approach is evaluated on more than 50 problems containing up to 288 assets, and the computational results

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provide evidence of its efficiency in two aspects: precision of solution and required computing time.

It is found that income tax has a clear impact on portfolio optimization for investors, which supports the conclusion from existing theoretical work. It also shows that with real trading constraints, tax rates and portfolio composition have a complex relationship that is neither linear nor convex. Convexity assumptions often made in the literature to guarantee global optimality, therefore, are not only unrealistic but also erroneous simplifications. This is the main advantage of my work over prior theoretical research on post-tax portfolio optimization. In addition, in the investigation on effects of withdrawal tax, it is found that for single-period optimization, this factor has a very limited influence. Investors can simplify the optimization model by ignoring withdrawal tax without changing the optimal solution significantly. Finally, the analysis proves that investors’ preference for certain assets is significantly influenced by taxation. Governments should estimate its quantitative effects before carrying out a new tax policy to avoid an unexpected capital outflow or excessive demand in relevant financial products.

6.2 Tobin Tax in Global Financial Markets

In Chapter 4, to investigate the impact of Tobin tax capital flows between regional markets, a post-tax portfolio optimization model with non-linear trading constraints and objective function is developed. To undertake a better examination of the influence of heterogeneous withholding and Tobin tax on international financial markets, almost all the real-world trading constraints are considered in the model. These include the need for diversification, requirements for both the number of assets in a portfolio and the maximum holdings in single assets, annual tax, deferred capital gains tax and taxation on cash withdrawals. So, investor behaviour can be simulated better. This influence is

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quantified by observing the rebalancing activities of rational investors under different tax settings.

Regarding the comparison between residence- and source-based taxes on internatinoal investments, it is found that the global optimal portfolio is highly sensitive to a change in regional investment tax rates. This sensitivity depends on the size of the change, market specifications and the international investment tax environment (residence only, source only or mixed tax). In a pure tax environment, the source only tax union will on average have more capital transits in international markets than the residence only tax union, and its optimal market portfolio will be more sensitive to regional tax policy changes. In a mixed tax system, double taxation between residence- and source-taxed markets will significantly reduce the attractiveness of the latter while the credit method will perform much better (increasing the attractiveness of the market with a source-based tax by up to 20%). In addition, experimental results suggest that volatile markets are usually accompanied by less unrealized capital gains and therefore are more sensitive to a government's tax policy than trending markets.

As regards the Tobin tax, market trading volume from rebalancing activities of rational investors (who seek to maximize the net Sharpe ratio) is highly sensitive to the implementation of Tobin tax. This sensitivity not only varies by market specifications but also varies by investment tax rules. A volatile market in a “Mixed with credit method” tax environment will be more sensitive to Tobin tax than a trending market in a “Mixed with double taxation” tax environment. Furthermore, experiments show that the capital locking effects of Tobin tax is mainly dependent on its effective rate but not the side of taxation (tax is levied on capital inflow only, outflow only, or both) if a consistent Tobin tax rule is applied globally. When the rule is heterogeneous across countries, for the market with relatively high Tobin tax rate, inflow Tobin tax will have a much higher capital lock-out effect, and outflow Tobin tax will have a much higher

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capital lock-in effect, in comparison to a consistent Tobin tax system across countries. In other words, the capital locking effect of Tobin tax is enlarged significantly when heterogeneous Tobin tax rates are applied globally. As a result, it will be very helpful if all countries can reach a deal on the implementation of Tobin tax. Otherwise the relatively high Tobin tax will significantly reduce the attractiveness of the local market to overseas investors.

6.3 Tax Arbitrage Optimization

In Chapter 5, to investigate tax arbitrage opportunities and therefore post-tax asset pricing, two improved continuous-time models for after-tax portfolio optimization are proposed. One applies to assets with perfect correlation and the other applies to uncorrelated assets with caps and floors. It is assumed that asset returns are continuous over time and use the Brownian motion process to simulate market prices. Both capital gains tax and income tax are included, and differential taxation for investors with long and short positions is also considered.

For correlated assets, the work of Basak and Croitorn (2001) is extended by including tax on capital gains. In contrast to their analysis which mainly concerns market equilibrium when no global tax arbitrage opportunity exists, mathematical constraints on tax rates and asset parameters (i.e. asset price, variance and expected return) are determined in this thesis to prove the existence of global tax arbitrage opportunities with no restriction on capital gains and income. An arbitrage portfolio between correlated assets can be achieved when all constrains are satisfied. Since income must be positive while capital gains could be either positive or negative, it is more difficult to prove the existence of arbitrage opportunities with both capital gains tax and income tax than with income tax only. This improvement increases the level of complexity but is necessary for the analysis of tax arbitrage opportunities. It is