9879HW09_Chen_Weiyi.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "#### Student: Chen Weiyi, weiyi.alan.chen@gmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MTH9879 Homework 9\n",
    "\n",
    "Assigned: April 21, 2015.\n",
    "Due: May 5, 2015 by 6pm. \n",
    "\n",
    "Late homework **will not be accepted**.\n",
    "\n",
    "$$\n",
    "\\newcommand{\\supp}{\\mathrm{supp}}\n",
    "\\newcommand{\\E}{\\mathbb{E}}\n",
    "\\newcommand{\\Eof}[1]{\\mathbb{E}\\left[ #1 \\right]}\n",
    "\\def\\Cov{{ \\mbox{Cov} }}\n",
    "\\def\\Var{{ \\mbox{Var} }}\n",
    "\\newcommand{\\1}{\\mathbf{1} }\n",
    "\\newcommand{\\PP}{\\mathbb{P} }\n",
    "%\\newcommand{\\Pr}{\\mathrm{Pr} }\n",
    "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
    "\\newcommand{\\RR}{\\mathbb{R} }\n",
    "\\newcommand{\\DD}{\\mathbb{D} }\n",
    "\\newcommand{\\HH}{\\mathbb{H} }\n",
    "\\newcommand{\\spn}{\\mathrm{span} }\n",
    "\\newcommand{\\cov}{\\mathrm{cov} }\n",
    "\\newcommand{\\sgn}{\\mathrm{sgn} }\n",
    "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
    "%\\newcommand{\\HS}{\\mathrm{HS} }\n",
    "\\newcommand{\\trace}{\\mathrm{trace} }\n",
    "\\newcommand{\\LL}{\\mathcal{L} }\n",
    "%\\newcommand{\\LL}{\\mathrm{L} }\n",
    "\\newcommand{\\s}{\\mathcal{S} }\n",
    "\\newcommand{\\ee}{\\mathcal{E} }\n",
    "\\newcommand{\\ff}{\\mathcal{F} }\n",
    "\\newcommand{\\hh}{\\mathcal{H} }\n",
    "\\newcommand{\\bb}{\\mathcal{B} }\n",
    "\\newcommand{\\dd}{\\mathcal{D} }\n",
    "\\newcommand{\\g}{\\mathcal{G} }\n",
    "\\newcommand{\\p}{\\partial}\n",
    "\\newcommand{\\half}{\\frac{1}{2} }\n",
    "\\newcommand{\\T}{\\mathcal{T} }\n",
    "\\newcommand{\\bi}{\\begin{itemize}}\n",
    "\\newcommand{\\ei}{\\end{itemize}}\n",
    "\\newcommand{\\beq}{\\begin{equation}}\n",
    "\\newcommand{\\eeq}{\\end{equation}}\n",
    "\\newcommand{\\beas}{\\begin{eqnarray*}}\n",
    "\\newcommand{\\eeas}{\\end{eqnarray*}}\n",
    "\\newcommand{\\cO}{\\mathcal{O}}\n",
    "\\newcommand{\\cC}{\\mathcal{C}}\n",
    "\\newcommand{\\cF}{\\mathcal{F}}\n",
    "\\newcommand{\\cL}{\\mathcal{L}}\n",
    "\\newcommand{\\BS}{\\text{BS}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = \"red\">Homework is to be done by each student individually.  To receive full credit, you must email a completed copy of this iPython notebook to Yu Gan (yugan323@gmail.com), Fubo Shi (fubo.shi.baruch@gmail.com), and Tai-Ho Wang (tai-ho.wang@baruch.cuny.edu) by the due date and time.  All R-code must run correctly and solutions must be written up neatly in Markdown/LaTeX format.\n",
    "\n",
    "<font color=\"blue\">If you encounter problems with Markdown/LaTeX or iPython notebook, please contact your TAs Yu Gan and/or Fubo Shi.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. (12 points)\n",
    "Following Almgren and Chriss,  assume that the stock price $S_t$ evolves as\n",
    "\n",
    "$$\n",
    "dS_t = \\sigma\\,dZ_t\n",
    "$$\n",
    "\n",
    "and the price $\\tilde S_t$ at which we transact is given by\n",
    "\n",
    "$$\n",
    "\\tilde S_t = S_t - \\eta\\,v_t\n",
    "$$\n",
    "\n",
    "where $v_t:=-{\\dot x}_t$ is the rate of trading with $x_0 = X$ and $x_T = 0$.\n",
    "\n",
    "In the lecture slides, we showed that with a risk term that penalizes average VaR instead of variance, the risk-adjusted cost of trading associated with a given price path $\\{S_t\\}$ is given by\n",
    "\n",
    "$$\n",
    "C = \\int_0^T\\,(S_t - \\eta\\,v_t) dx_t + \\lambda\\,\\sigma\\,\\int_0^T\\,x_t\\,dt\n",
    "$$\n",
    "\n",
    "for some price of risk $\\lambda$. We want to find a (possibly state-dependent) control $v_t$ that minimizes the expected cost $\\cC=\\E[C]$.\n",
    "\n",
    "(a) Apply the technique of integration by parts to simplify the term $\\int_0^T S_t dx_t$. Write down the HJB equation for the resulting problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = 'darkblue'>\n",
    "\n",
    "### Solution\n",
    "\n",
    "Apply the technique of integration by parts,\n",
    "\n",
    "$$\n",
    "\\left.\\int_0^T S_t\\,dx_t =  S_t\\,x_t \\right\\vert_0^T - \\int_0^T x_t\\,dS_t = -XS -\\int_0^T\\sigma x_tdZ_t,\n",
    "$$\n",
    "we have\n",
    "$$\n",
    "\\E\\left[ \\int_0^T S_t\\,dx_t \\right] = -XS\n",
    "$$\n",
    "\n",
    "Then the controlled $v_t$ that minimizes the exptected cost $\\cC$ is\n",
    "\n",
    "\\begin{equation}\n",
    "v_t \n",
    "= \\mbox{argmin}_{v_t\\in\\mathcal G} \\,\\E\\left[\\cC\\right] \n",
    "= \\mbox{argmin}_{v_t\\in\\mathcal G} \\left\\{-XS + \\E\\left[\\int_0^T\\,\\eta\\,v_t^2 dt + \\lambda\\,\\sigma\\,\\int_0^T\\,x_t\\,dt\\right]\\right\\}\n",
    "\\end{equation}\n",
    "\n",
    "Now the deterministic optimal control problem is to solve this part,\n",
    "$$\n",
    "\\tilde C(t,x) = \\min_{v_t\\in\\mathcal G} \\left\\{\\E\\left[\\int_0^T\\,\\eta\\,v_t^2 dt + \\lambda\\,\\sigma\\,\\int_0^T\\,x_t\\,dt\\right]\\right\\}\n",
    "$$\n",
    "\n",
    "with corresponding HJB equation as\n",
    "$$\n",
    "\\frac{\\partial{\\tilde C}}{\\partial t} + \\lambda\\sigma x_t + \\min_{v_t\\in\\mathcal G} \\left\\{-\\tilde C_x v + \\eta v^2 \\right\\} = 0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Solve the first order condition to find the optimal trading rate $v^\\star$.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution\n",
    "\n",
    "Let \n",
    "$$ \\frac{\\partial}{\\partial v} (-\\tilde C_x v + \\eta v^2) = -\\tilde C_x + 2\\eta v = 0. $$\n",
    "\n",
    "The optimal trading rate $v^\\star$ is\n",
    "$$ v^\\star = \\frac{1}{2\\eta}\\tilde C_x. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) Substitute $v^\\star$ back into the HJB equation to show that the value function $\\cC$ must satisfy\n",
    "$$\n",
    "\\cC_t = \\frac{\\cC_x^2}{4\\,\\eta\\,} - \\lambda \\sigma x.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution\n",
    "\n",
    "Substitute $v^\\star$ back to HJB,\n",
    "\\begin{equation}\n",
    "    \\frac{\\partial{C}}{\\partial t} + \\lambda\\sigma x_t + \\left\\{-C_x \\cdot \\frac{1}{2\\eta}C_x + \\eta \\cdot \\frac{1}{4\\eta^2}C_x^2 \\right\\} = 0\n",
    "\\end{equation}\n",
    "\n",
    "Obviously,\n",
    "\n",
    "\\begin{equation}\n",
    "    \\cC_t = \\frac{\\cC_x^2}{4\\,\\eta\\,} - \\lambda \\sigma x.\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(d) With the terminal condition, \n",
    "$$\\lim_{t\\uparrow T}\\cC(t,x) = \\begin{cases}0&\\text{if $x=0$,}\\\\\n",
    "+\\infty&\\text{if $x\\neq0$.}\n",
    "\\end{cases}$$\n",
    "solve the HJB equaiton with the ansatz $\\cC(t,x) = a(t)x^2 + b(t)x + c(t)$. Verify that the optimal trading strategy with liquidation horizon set to the characteristic time is given by\n",
    "\\begin{eqnarray*}\n",
    "x_t&=&X\\,\\left(1-\\frac{t}{T}\\right)^2.\n",
    "\\end{eqnarray*}\n",
    "Recall that with the notation of the lecture slides, the characteristic time is defined as\n",
    "$$\n",
    "T^\\star=\\sqrt{\\frac{2\\,X}{A}}=\\sqrt{\\frac{4\\,\\eta\\,X}{\\lambda\\,\\sigma}}\n",
    "$$\n",
    "Compute the risk-adjusted cost function $\\cC$ associated with this strategy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution\n",
    "\n",
    "In the lecture notes, we have\n",
    "$$ x_t = X\\left( 1 - \\frac{t}{T}\\right)^2, v_t = -\\dot{x}_t = \\frac{2X}{T}\\left( 1 - \\frac{t}{T}\\right) $$\n",
    "\n",
    "By substituting them into the cost function, we finally derive\n",
    "\\begin{equation}\n",
    "\\cC(t,x) \n",
    "= \\int_t^T \\lambda\\sigma\\,x_s\\,ds+\\lambda\\sigma\\int_t^T x_s\\,ds \n",
    "= \\frac{2\\lambda\\sigma T }{3X^{\\frac{1}{2}}}x_t^{\\frac{3}{2}}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ABM and GBM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up R environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext rpy2.ipython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/MSFT130311.rData_.zip'\n",
       "Content type 'application/zip' length 71919 bytes (70 KB)\n",
       "opened URL\n",
       "==================================================\n",
       "downloaded 70 KB\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "library(highfrequency)\n",
    "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/MSFT130311.rData_.zip\", destfile=\"MSFT130311.zip\")\n",
    "unzip(zipfile=\"MSFT130311.zip\")\n",
    "load(\"MSFT130311.rData\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. (8 points)\n",
    "\n",
    "Recall from the lecture slides that with time-averaged VaR as the risk penalty, and when the liquidation time $T$ is chosen to be the characteristic time, the optimal trading rate under ABM becomes\n",
    "\n",
    "$$\n",
    "v^A(t)= \\frac{x_t}{T-t}\\,+\\frac{X}{T}\\,\\left(1-\\frac t T\\right)\n",
    "$$\n",
    "\n",
    "and the optimal trading rate under GBM becomes\n",
    "\n",
    "$$\n",
    "v^G(t)= \\frac{x_t}{T-t}\\,+\\frac{X}{T}\\,\\frac{S_t}{S_0}\\,\\left(1-\\frac t T\\right).\n",
    "$$\n",
    "\n",
    "(a) The *msft.bats* dataset from *MSFT130311.rData* contains all trades on the BATS exchange on 11-Mar-2013.  One trading days has 390 minutes.  Sample the  *msft.bats* dataset evenly, roughly every minute of volume time.  Superimpose plots of the optimal strategy under ABM and GBM assuming liquidation takes place over one trading day."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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NGoS+fftiyJAhSE9PR5kyZbBr1y4sWrQIJihr7NixUedpcV8aW9cjnN4YWEcxrlEdWL3W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\nJLYAATix64fcIYAAAgikqEDA2CVFyxZSrI0bN8p1110n+qUfrVkqKys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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HrIsvvti7NV28ePH86uHts05c9pNbmjdvnndlndu+omw78khpxgypfXu/Y1a3bnI9tyUb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\nzTffqHv37mrUqJE6dOigN954I+PDmGdQRPXF999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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bNGnyzDfW/VH8S85iiQS04tih5uYVGCtVw4xT/cXxw2TMSXgdy+PbI8I7GEti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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "\n",
    "# initialization\n",
    "\n",
    "df <- msft130311.bats    # The msft.bats dataset from MSFT130311.rData\n",
    "i_T <- 390               # One trading days has 390 minutes, liquidation time T\n",
    "i_X <- 10000             # initial positions\n",
    "ls_timeStamp <- c(1:i_T)   # list of time stamps to use later\n",
    "\n",
    "# prepare metrics\n",
    "\n",
    "df$sum <- cumsum(abs(df$signed.shares))     # cumulative sum of shares number\n",
    "i_numTrade <- length(df$sum)                # total number of trades\n",
    "i_totalVol <- df$sum[i_numTrade]              # total volumn\n",
    "\n",
    "# sample the msft.bats dataset evenly, roughly every minute of volume time\n",
    "\n",
    "ls_samples <- seq(1, i_totalVol, i_totalVol/i_T)\n",
    "\n",
    "# construct a list of sample index\n",
    "\n",
    "ls_index <- c(1:length(ls_samples))\n",
    "j = 1\n",
    "for (i in 1:i_numTrade) {\n",
    "    if (df$sum[i] > ls_samples[j] && j <=390) {\n",
    "        ls_index[j] = i\n",
    "        j = j+1\n",
    "    }\n",
    "}\n",
    "\n",
    "# construct price series S_t, position list and trading rate list\n",
    "ts_price <- df[ls_index, 'trade.price']\n",
    "\n",
    "ls_xABM <- c(0:i_T)\n",
    "ls_rABM <- c(1:i_T) \n",
    "ls_xABM[1] = i_X\n",
    "\n",
    "ls_xGBM <- c(0:i_T)\n",
    "ls_rGBM <- c(1:i_T) \n",
    "ls_xGBM[1] = i_X\n",
    "\n",
    "\n",
    "# calculate trading rate and positions\n",
    "\n",
    "for (t in 1:i_T){\n",
    "    ls_rABM[t] = abs(ls_xABM[t])/(i_T - t) + i_X / i_T * (1 - t/i_T)\n",
    "    ls_xABM[t+1] = max(ls_xABM[t] - ls_rABM[t], 0)\n",
    "    \n",
    "    ls_rGBM[t] = abs(ls_xGBM[t])/(i_T - t) + i_X / i_T * ts_price[t]/ts_price[1] * (1 - t/i_T)\n",
    "    ls_xGBM[t+1] = max(ls_xGBM[t] - ls_rGBM[t], 0)\n",
    "}\n",
    "\n",
    "# plot the trading rate\n",
    "plot(ls_timeStamp, ls_rABM, xlab = \"Time Stamps\", ylab = \"Trading Rates\", col = \"red\", type = \"p\", main = 'ABM')\n",
    "plot(ls_timeStamp, ls_rGBM, col = \"blue\", type = \"l\", lwd = 3, main='GBM')\n",
    "\n",
    "plot(ls_timeStamp, ls_rABM, xlab = \"Time Stamps\", ylab = \"Trading Rates\", col = \"red\", type = \"p\", main = 'ABM & GBM')\n",
    "lines(ls_timeStamp, ls_rGBM, col = \"blue\", type = \"l\", lwd = 3)\n",
    "legend(\"topright\", c(\"ABM\",\"GBM\"), col = c(\"red\",\"blue\"), lwd = 2, inset = 0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Denote the corresponding position sizes by $x^A(t)$ and $x^G(t)$ respectively.  What is the maximum deviation of the two position sizes as a percentage of the initial position $X$?  How significant is this deviation?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1] 0.1228432\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "# the maximum deviation of the two position sizes as a percentage of the initial position\n",
    "ls_deviations <- sapply(ls_timeStamp, function(t)(ls_xGBM[t] - ls_xABM[t])/i_X*100.)\n",
    "f_maxDev <- max(ls_deviations)\n",
    "print(f_maxDev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "The maximum deviation of the two position sizes as a percentage of the initial position $X$ is 0.1228%. That's very small so it is not significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kratz and Schöneborn with time-averaged VaR risk charge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. (16 points)\n",
    "\n",
    "(a) Repeat the computation of the optimal strategy from the lecture slides with time-averaged VaR\n",
    "\n",
    "$$\n",
    "\\lambda\\,\\sigma\\,\\int_0^T\\,x_t\\,dt\n",
    "$$\n",
    "\n",
    "as the risk term (rather than the quadratic variation $\\lambda\\,\\sigma^2\\,\\int_0^T\\,x_t^2\\,dt$).  Show that the optimal position\n",
    "\n",
    "$$\n",
    "x^\\star(t)=\\left(X-\\frac{A\\, T}{\\theta }\\right)\\,\\frac{1-e^{-\\theta\\,(T-t)} }{1-e^{-\\theta\\,T }}+\\frac{A }{\\theta }\\,(T-t)\n",
    "$$\n",
    "and deduce the optimal trading rate $v^\\star(t)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='darkblue'>\n",
    "\n",
    "### Solution\n",
    "\n",
    "As before, the expected cost of liquidation (with risk penalty) is given\n",
    "(as of time $t$) by\n",
    "\n",
    "$$\\mathcal{C} (t)=\\eta\\,\\mathbb{E} \\left[\\int_t^T\\, (\\dot x_u^2+\\kappa^2\\,x_u^2)\\,du\\right]$$\n",
    "\n",
    "with $$\\kappa^2=\\frac{\\lambda\\,\\sigma^2}{\\eta}.$$\n",
    "\n",
    "In our case,\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\mathcal{C} = \\eta\\,\\E\\left[\\,\\int_0^T\\,({\\dot x}_t^2 + \\frac{\\lambda\\sigma}{\\eta}x_t) 1_{t < t*}\\,dt\\right]\n",
    "= \\eta\\,\\int_0^T\\,({\\dot x}_t^2 + \\frac{\\lambda\\sigma}{\\eta}x_t) e^{-\\theta t}\\,dt\n",
    "\\end{eqnarray*}\n",
    "\n",
    "Apply Kratz-Schöneborn HJB equation, we derive \n",
    "\n",
    "$$\n",
    "\\frac{d}{dt}(2\\dot{x}_te^{-\\theta t}) - \\frac{\\lambda\\sigma}{\\eta}e^{-\\theta t} = 0 \\Rightarrow\\,\\, \\ddot{x}_t - \\theta\\dot{x}_t - \\frac{\\lambda\\sigma}{2\\eta} = 0\n",
    "$$\n",
    "\n",
    "Given the boundary conditions as $X_0 = X$, $X_T = 0$ and denote $A = \\frac{\\lambda\\sigma}{2\\eta}$, we have the solution of the ODE\n",
    "\n",
    "$$ x^\\star(t)=\\left(X-\\frac{A\\, T}{\\theta }\\right)\\,\\frac{1-e^{-\\theta\\,(T-t)} }{1-e^{-\\theta\\,T }}+\\frac{A }{\\theta }\\,(T-t) $$\n",
    "\n",
    "The optimal trading rate is\n",
    "$$\n",
    "v^\\star(t)= -\\dot x^\\star(t) = \\theta(X-\\frac{AT}{\\theta})\\frac{e^{-\\theta(T-t)}}{1-e^{-\\theta T}} + \\frac{A}{\\theta}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) By Taylor-expanding the solution around $\\theta=0$, show that we retrieve the solution derived in the slides with no dark pool\n",
    "\n",
    "$$\n",
    "x^\\star(t)=\\left(X-\\frac{A \\, T}{2}\\,t\\right)\\,\\left(1-\\frac{t}{T}\\right) .\n",
    "$$\n",
    "\n",
    "in the limit $\\theta \\to 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = \"darkblue\"> \n",
    "\n",
    "### Solution\n",
    "\n",
    "By Taylor-expanding the solution around $\\theta = 0$,\n",
    "\\begin{eqnarray*}\n",
    "x^\\star(t) &\\approx& \\left(X-\\frac{A\\, T}{\\theta }\\right)\\,\\frac{(T-t)\\theta-\\frac{1}{2}(T-t)^2\\theta^2}{T\\theta - \\frac{1}{2}T^2\\theta^2}+\\frac{A }{\\theta }\\,(T-t)\\\\\n",
    "&=& \\left(X-\\frac{A\\, T}{\\theta }\\right)\\,\\frac{(T-t)-\\frac{1}{2}(T-t)^2\\theta}{T - \\frac{1}{2}T^2\\theta}+\\frac{A }{\\theta }\\,(T-t)\\\\\n",
    "\\end{eqnarray*}\n",
    "\n",
    "For the part with $X$,\n",
    "\n",
    "\\begin{eqnarray}\n",
    "X \\frac{(T-t)-\\frac{1}{2}(T-t)^2\\theta}{T - \\frac{1}{2}T^2\\theta} & \\approx & X\\frac{T-t}{T} = X(1-\\frac{t}{T})\n",
    "\\end{eqnarray}\n",
    "\n",
    "For the others,\n",
    "\n",
    "\\begin{eqnarray}\n",
    "-\\frac{AT}{\\theta} \\frac{(T-t)-\\frac{1}{2}(T-t)^2\\theta}{T - \\frac{1}{2}T^2\\theta} +\\frac{A }{\\theta }\\,(T-t)\n",
    "&=& - A(T-t)\\left[\\frac{1-\\frac{1}{2}(T-t)\\theta}{\\theta(1-\\frac{1}{2}T\\theta)} - \\frac{1}{\\theta}\\right] \\\\\n",
    "&=& - A(T-t)\\left[\\frac{\\frac{1}{2}t}{1-\\frac{1}{2}T\\theta} \\right]\\\\\n",
    "&\\approx& - \\frac{A(T-t)t}{2}\\\\\n",
    "&=& \\left(-\\frac{AT}{2}t \\right)\\,\\left(1-\\frac{t}{T} \\right)\n",
    "\\end{eqnarray}\n",
    "\n",
    "Therefore aggregating together,\n",
    "\n",
    "$$\n",
    "x^\\star(t)=\\left(X-\\frac{A \\, T}{2}\\,t\\right)\\,\\left(1-\\frac{t}{T}\\right) .\n",
    "$$"
   ]
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